Ocean Energy Safety and Technology Improvement Act of 2013 - Amends the Outer Continental Shelf Lands Act, with respect to the consideration of permits for geological explorations and development and production, to allow the Secretary of the Interior to give priority to reviewing and processing plans and applications that use, develop, or demonstrate new safety-enhancing technologies.
Directs the Secretary to establish: (1) a small business innovation research program or technology transfer program, or both, to broaden participation in the development of safer technologies for offshore oil and gas exploration and development; and (2) an Ocean Energy Safety Institute, as a collaborative federally funded research and development center or university-affiliated research center, to enhance safe and responsible operations across the offshore oil and gas industry. Funds operations of the Institute through an annual fee applicable to areas of the outer Continental Shelf subject to an oil or gas lease under which production is not occurring.