Robert William Gillespie (October 8, 1919 – November 4, 2001) was an American pitcher in Major League Baseball who played between 1944 and 1950 for the Detroit Tigers (1944), Chicago White Sox (1947–48) and Boston Red Sox (1950).

The native of Columbus, Ohio, served in the United States Coast Guard during World War II.

In a four-season career, Gillespie posted a 5–13 record with a 4.73 ERA in 58 pitching appearances, including 23 starts, two complete games, 59 strikeouts, 102 walks, and 202 ⅓ innings of work.

Gillespie died in Winston-Salem, North Carolina on November 4, 2001, at the age of 82.

This biographical article relating to an American baseball pitcher born in the 1910s is a stub.