Marine Resource Management and Research Act - Establishes in the Treasury the Marine Resource Management and Research Fund. Provides revenues for such Fund from Outer Continental Shelf oil and gas leases (ten percent of the difference between the current fiscal year and FY 1981, with a $300,000,000 annual maximum).

Allocates from such Fund beginning with FY 1984: (1) 30 to 40 percent for coastal zone management; (2) 15 to 25 percent for the sea grant program; and (3) ten to 20 percent for anadromous fish and commercial fisheries. Makes unallocated funds available for other State marine resource education, management, and research programs.

Requires a State to have implemented a federally approved coastal zone management program and to have submitted a related report to the Secretary of Commerce to qualify for such coastal zone management grant.

Requires the Secretary to submit to the President and the Congress within one year a National Coastal Zone and Fishery Management Research Plan. States that such Plan shall include measures for the conservation, management, and research of the entire coastal zone and of coastal dependent migratory fish. Requires public hearings before submittal. Makes the Plan effective on October 1, 1983, unless vetoed by a resolution of either House of Congress within 60 days after submittal.