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. U.S. Army Private, World War I. He was a Secretary to Justices McLaughlin and Finch, Supreme Court of New York in 1911. He was an Assistant district attorney of New York County, New York from 1914 to 1916. He was a Justice, Municipal Court, 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.
Coleman was a federal judge on the United States District Court for the Southern District of New York. Coleman received a recess appointment from Calvin Coolidge on May 19, 1927, to a seat vacated by Augustus N. Hand. Formally nominated on December 6, 1927. He was confirmed by the United States Senate on December 19, 1927, and received his commission the same day. Coleman served in that capacity until March 14, 1934, due to his death.