Career wise, that would be Tony Gwynn (1982-2001) with a .338 career average. As of the start of the 2008 season, Gwynn ranks 20th all time in MLB career batting average. For a single season, that would be George Brett (1973-1993) with a .390 average in the 1980 season.
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In the history of Major League Baseball as of 2009 there are 202 players with a career batting average of .300 or better.
Riggs Stephenson and Bill Madlock are tied for the Cubs career batting average leader with .336.
As of the start of the 2009 season, the active MLB player with the highest batting average is Albert Pujols of the St. Louis Cardinals at .334. Ichiro Suzuki of the Mariners is second at .331 and Todd Helton of the Rockies is third at .328.The highest all time career MLB batting average is Ty Cobb at .366.Now its Derek jeter in 2009 with .400
Hall of Famer George Brett of the Kansas City Royals won the American League batting title in 1976, 1980, and 1990. He's the only player in baseball history to win the batting title in three differnt decades.
Hugh Duffy of the 1894 Boston Beaneaters.