Frank Joseph Coleman (March 24, 1886 – March 14, 1934) was a United States federal judge.
Born in New York, New York, Coleman received an A.B. from City College of New York in 1906 and an LL.B. from New York Law School in 1909. He was a secretary to Justice McLaughlin and Justice Finch of the Supreme Court of New York in 1911, and then became an assistant district attorney of New York County, New York from 1914 to 1916. He served as a Private in the United States Army during World War I. He was a Justice of the Municipal Court of New York City from 1918 to 1923. He was a Republican leader of 15th assembly district, New York County, New York from 1924 to 1927.
On May 19, 1927, Coleman received a recess appointment from Calvin Coolidge to a seat on the United States District Court for the Southern District of New York vacated by Augustus N. Hand. Formally nominated on December 6, 1927, Coleman was confirmed by the United States Senate on December 19, 1927, and received his commission the same day. He served in that capacity until his death.