Has university of Texas ever won national championship in basketball?

No, the University of Texas (Austin-Longhorns) has never won a NCAA Basketball Championship. In fact the only university or college that has won a Championship in the state of Texas is UTEP (The University of Texas at El Paso) in 1966. The legendary hall of fame coach Don Haskins "The Bear" started for the first time 5 African-American players and made history beating the arrogant all-white Kentucky Wildcats. Until that moment, at the height of the civil-rights era, no major-college team had ever started five African American players in an NCAA championship game. In fact, until Texas Western coach Don Haskins did it earlier that season, no major-college team had ever started five blacks in ANY game.

UTEP was called Texas Western at the time.

The final score was: Texas Western Miners 72 Kentucky Wildcats 65

Some analysts say that this was the most important moment in College Sports. Disney made a really good movie about this: Glory Road.