Born in Providence, RI in 1868, Groves attended Cornell University and received a degree in architecture in 1888. Two subsequent years of work for Denver architect F. E. Edbrooke were followed by study and travel in France and Italy. Groves came to St. Louis in 1891 as a draftsman for Grable & Weber. The firm was one of the best established in the city with clients in Vandeventer Place and other exclusive residential areas. By 1895, he had become a partner in Grable, Weber & Groves. Three years later, the younger partners bought out Grable´s interest and the firm continued as Weber & Groves until Weber´s death in 1905. One of that partnership´s last important commissions was the 1904 rotunda at City Hall.

Groves practiced on his own until his death in 1925. His commissions from those twenty years represent one of the most diverse and prolific portfolios of any early 20th century St. Louis architect. His building at 8th and Pine is one of downtown´s overlooked treasures. Designed by Groves in 1907, the rich terra cotta ornament from Winkle Terra Cotta Company and the fine apricot-colored brickwork triumph over layers of grime and signs.

Churches designed by Groves include the Union Avenue Christian, Westminster Presbyterian, St. Paul´s Presbyterian, Maple Avenue Methodist and Christian Science Churches on Russell near Grand and Page west of Union. Groves´ first large commission in Midtown was the St. Louis Medical Society Building on Lindell; his last, with Thomas C. Young of Eames & Young, was the monumental Masonic Temple that was under construction at the time of his death in 1925.

Groves married Clara Baker of St. Charles in 1892. His eldest son, Theron, had entered his father´s office by the early 1920s and continued the practice as Albert B. Groves, Inc. from the family home at 5419 Maple until 1939. That house, described in 1910 as English manor style of the Tudor period, is still standing.