Initially a referee, Curtis took up his first managerial post with Kent side Gillingham in 1923, but left three years later when the board refused his request for a pay rise. Curtis joined Brentford almost immediately and proceeded to transform the club's fortunes. He led them to the Division Three South title in 1932-33 and the Second Division title in 1934-35. In their debut season in the First Division, Curtis guided the Bees to a 5th place finish, making them the highest-placed team from London, followed by two 6th place finishes.
During the Second World War, Brentford won the London War Cup, beating Portsmouth in the final at Wembley. Curtis remained manager until 1949, by which time the club had been relegated. He remains Brentford's most successful and longest-serving manager.