SCHEDULE 13G

Amendment No. 0
MoneyGram International, Inc.
Common Stock
Cusip #60935Y109


Cusip #60935Y109
Item 1:	Reporting Person - FMR Corp.
Item 4:	Delaware
Item 5:	1,800
Item 6:	0
Item 7:	4,750,359
Item 8:	0
Item 9:	4,750,359
Item 11:	5.364%
Item 12:	    HC


Cusip #60935Y109
Item 1:	Reporting Person - Edward C. Johnson 3d
Item 4:	United States of America
Item 5:	0
Item 6:	0
Item 7:	4,750,359
Item 8:	0
Item 9:	4,750,359
Item 11:	5.364%
Item 12:	IN


Cusip #60935Y109
Item 1:	Reporting Person - Abigail P. Johnson
Item 4:	United States of America
Item 5:	0
Item 6:	0
Item 7:	4,750,359
Item 8:	0
Item 9:	4,750,359
Item 11:	5.364%
Item 12:	    IN



	SCHEDULE 13G - TO BE INCLUDED IN
STATEMENTS
	FILED PURSUANT TO RULE 13d-1(b) or 13d-2(b)




Item 1(a).	Name of Issuer:

		MoneyGram International, Inc.

Item 1(b).	Name of Issuer's Principal Executive Offices:

		1550 Utica-Avenue South
		Suite 100
		Minneapolis, Minnesota  55416


Item 2(a).	Name of Person Filing:

		FMR Corp.

Item 2(b).	Address or Principal Business Office or, if None,
Residence:

		82 Devonshire Street, Boston,
Massachusetts  02109

Item 2(c).	Citizenship:

		Not applicable

Item 2(d).	Title of Class of Securities:

		Common Stock

Item 2(e).	CUSIP Number:

		60935Y109

Item 3.	This statement is filed pursuant to Rule 13d-1(b) or 13d-2(b)
and the person filing, FMR Corp., is a parent holding company
in accordance with Section 240.13d-1(b)(ii)(G).  (Note:  See
Item 7).

Item 4.	Ownership

	(a)	Amount Beneficially Owned:	4,750,359

	(b)	Percent of Class:	5.364%

	(c)	Number of shares as to which such
person has:

	(i)	sole power to vote or to direct
the vote:	1,800

	(ii)	shared power to vote or to
direct the vote:	0

	(iii)	sole power to dispose or to
direct the disposition of:	4,750,359

	(iv)	shared power to dispose or to
direct the disposition of:	0



Item 5.	Ownership of Five Percent or Less of a Class.

	Not applicable.

Item 6.	Ownership of More than Five Percent on Behalf of Another
Person.

	Various persons have the right to receive or the power to
direct the receipt of dividends from, or the proceeds from the
sale of, the Common Stock of MoneyGram International, Inc..
No one person's interest in the Common Stock of MoneyGram
International, Inc. is more than five percent of the total
outstanding Common Stock.

Item 7.	Identification and Classification of the Subsidiary Which
Acquired the Security Being Reported on By the Parent
Holding Company.

	See attached Exhibit(s) A, B.

Item 8.	Identification and Classification of Members of
the Group.

	Not Applicable. See attached Exhibit A.

Item 9.	Notice of Dissolution of Group.

	Not applicable.

Item 10.	Certification.

	By signing below I certify that, to the best of my knowledge
and belief, the securities referred to above were acquired in the
ordinary course of business and were not acquired for the
purpose of and do not have the effect of changing or
influencing the control of the issuer of such securities and
were not acquired in connection with or as a participant in any
transaction having such purpose or effect.

Signature

	After reasonable inquiry and to the best of my knowledge and
belief, I certify that the information set forth in this Schedule
13G in connection with FMR Corp.'s beneficial ownership of
the Common Stock of MoneyGram International, Inc. at
December 31, 2004 is true, complete and correct.

February 14, 2005
Date

/s/Eric D. Roiter
Signature

Eric D. Roiter
Duly authorized under Power of Attorney
dated December 30, 1997 by and on behalf
of FMR Corp. and its direct and indirect
subsidiaries


	SCHEDULE 13G - TO BE INCLUDED IN
STATEMENTS
	FILED PURSUANT TO RULE 13d-1(b) or 13d-2(b)



	Pursuant to the instructions in Item 7 of Schedule
13G, Fidelity Management & Research Company
("Fidelity"), 82 Devonshire Street, Boston, Massachusetts
02109, a wholly-owned subsidiary of FMR Corp. and an
investment adviser registered under Section 203 of the
Investment Advisers Act of 1940, is the beneficial owner of
4,748,559 shares or 5.362% of the Common Stock
outstanding of MoneyGram International, Inc.  ("the
Company") as a result of acting as investment adviser to
various investment companies registered under Section 8 of
the Investment Company Act of 1940.

	Edward C. Johnson 3d, FMR Corp., through its
control of Fidelity, and the funds each has sole power to
dispose of the 4,748,559 shares owned by the Funds.

	Neither FMR Corp. nor Edward C. Johnson 3d,
Chairman of FMR Corp., has the sole power to vote or direct
the voting of the shares owned directly by the Fidelity Funds,
which power resides with the Funds' Boards of Trustees.
Fidelity carries out the voting of the shares under written
guidelines established by the Funds' Boards of Trustees.

	Fidelity Management Trust Company, 82 Devonshire
Street, Boston, Massachusetts 02109, a wholly-owned
subsidiary of FMR Corp. and a bank as defined in Section
3(a)(6) of the Securities Exchange Act of 1934, is the
beneficial owner of  1,000 shares or 0.001% of the Common
Stock outstanding of the Company as a result of its serving as
investment manager of the institutional account(s).

	Edward C. Johnson 3d and FMR Corp., through its
control of Fidelity Management Trust Company, each has
sole dispositive power over 1,000 shares and sole power to
vote or to direct the voting of 1,000 shares of Common Stock
owned by the institutional account(s) as reported above.

	Strategic Advisers, Inc., 82 Devonshire Street,
Boston, MA 02109, a wholly-owned subsidiary of FMR
Corp. and an investment adviser registered under Section 203
of the Investment Advisers Act of 1940, provides investment
advisory services to individuals.  As such, FMR Corp.'s
beneficial ownership includes 800 shares, or 0.001%, of the
Common Stock stock outstanding of MoneyGram
International, Inc., beneficially owned through Strategic
Advisers, Inc.

	Members of the Edward C. Johnson 3d family are the
predominant owners of Class B shares of common stock of
FMR Corp., representing approximately 49% of the voting
power of FMR Corp.  Mr. Johnson 3d owns 12.0% and
Abigail Johnson owns 24.5% of the aggregate outstanding
voting stock of FMR Corp.  Mr. Johnson 3d is Chairman of
FMR Corp. and Abigail P. Johnson is a Director of FMR
Corp.  The Johnson family group and all other Class B
shareholders have entered into a shareholders' voting
agreement under which all Class B shares will be voted in
accordance with the majority vote of Class B shares.
Accordingly, through their ownership of voting common
stock and the execution of the shareholders' voting
agreement, members of the Johnson family may be deemed,
under the Investment Company Act of 1940, to form a
controlling group with respect to FMR Corp.




	SCHEDULE 13G - TO BE INCLUDED IN
STATEMENTS
	FILED PURSUANT TO RULE 13d-1(b) or 13d-2(b)
	RULE 13d-1(f)(1)  AGREEMENT

	The undersigned persons, on February 14, 2005, agree
and consent to the joint filing on their behalf of this Schedule
13G in connection with their beneficial ownership of the
Common Stock of MoneyGram International, Inc. at
December 31, 2004.

	FMR Corp.

	By /s/ Eric D. Roiter
	Eric D. Roiter
	Duly authorized under Power of Attorney
	dated December 30, 1997, by and on behalf
	of FMR Corp. and its direct and indirect
	subsidiaries

	Edward C. Johnson 3d

	By /s/ Eric D. Roiter
	Eric D. Roiter
	Duly authorized under Power of Attorney
	dated December 30, 1997, by and on behalf
	of Edward C. Johnson 3d

	Abigail P. Johnson

	By /s/ Eric D. Roiter
	Eric D. Roiter
	Duly authorized under Power of Attorney
	dated December 30, 1997, by and on behalf
	of Abigail P. Johnson

	Fidelity Management & Research Company

	By /s/ Eric D. Roiter
	Eric D. Roiter
	Senior V.P. and General Counsel