James Henry Mays (June 29, 1868 - April 19, 1926) was a U.S. Representative from Utah.

Born in Morristown, Tennessee, Mays attended the district schools. He moved to Kansas in 1883 with his parents, who settled in Galena, Kansas. He worked in the mines and as a lumberman. He attended the Kansas State Normal School. From 1893 to 1902 engaged in the life insurance business at Chicago, Illinois, Dubuque, Iowa, and Salt Lake City, Utah. He was graduated from the law department of the University of Michigan at Ann Arbor in 1895. He was admitted to the bar and commenced practice in Ann Arbor, Michigan. He moved to Indianapolis, Indiana, in 1896 and to Utah in 1902. Organized several industrial organizations.

Mays was elected as a Democrat to the Sixty-fourth, Sixty-fifth, and Sixty-sixth Congresses (March 4, 1915-March 3, 1921). He was not a candidate for reelection in 1920. He retired to his stock ranch near Wendell, Idaho, and died there on April 19, 1926. He was interred in Gooding Cemetery, Gooding, Idaho.