Was there a black person in the USA that ran for president besides Barack Obama?

Jesse Jackson, Sr. was the first person of African descent to campaign for a major-party presidential nomination, in 1984 (the Democratic Party).

Jesse Jackson competed for the Democratic Party Presidential Nomination again in 1988.

Alan Keyes campaigned for the Republican Party Presidential Nomination in 1996, 2000 and 2008.

Herman Cain campaigned for the Republican Party Presidential Nomination in 2000 and 2012.

Al Sharpton and Carol Moseley Braun campaigned for the Democratic Party Presidential Nomination in 2004.

On August 27, 2008, Barack Obama officially became the first person of African descent to receive a major-party U.S. Presidential Nomination.