William Briley Greif (born April 25, 1950) is a retired professional baseball pitcher.

He played all or part of six seasons in Major League Baseball, from 1971 to 1976, for the Houston Astros, San Diego Padres, and St. Louis Cardinals.

He was traded along with Derrel Thomas and Mark Schaeffer from the Astros to the Padres for Dave Roberts on December 3, 1971.

A knuckle-curve specialist, he was the team's Opening Day starter in 1974, then in 1975 he was moved full-time to the bullpen.

He was sent along with Sam Mejías and Ángel Torres from the Cardinals to the Montreal Expos for Tony Scott, Steve Dunning and Pat Scanlon on November 8, 1976.