Here is how Wikipedia describes its funding:
The Center is a public-private partnership. Approximately one third of the Center's operating funds come annually from an appropriation from the U.S. government, and the Center's building, a wing of the Ronald Reagan Building, was provided by the U.S. government. The remainder of the Center's funding comes from foundations, grants and contracts, corporations, individuals, endowment income, and subscriptions.The Board of Trustees are appointed to six-year terms by the US President. The Board is made up of private citizens (businessmen, lawyers, professors, etc...) and public members, who currently include Secretary of State Hillary Clinton, Education Secretary Arne Duncan, and HHS Secretary Kathleen Sebelius, among others.
Based on the latest publicly available records, the Wilson Center has assets of around $106 million.
Click here to see the Wilson Center's budget justifications for fiscal year 2013 that is presented to the US Congress, in which it asked for $10.492 million.
The document notes that funding support has come from, among others, both large and small foundations such as the Carnegie Corporation, MacArthur Foundation, Connect US Fund, and Leon Levy Foundation. It notes that because of "challenging economic conditions," foundation endowments to the Center have declined.
It was announced in February 2011 that [former] Rep. Jane Harman (D-CA) was appointed to be the Wilson Center's new head. She resigned from Congress on February 28, 2011 to join the Center as its first female Director, President, and CEO.
Harman is also on the Board of Trustees of the Aspen Institute.