Billy Grassam played his early football in Scotland. In 1897 he joined Maryhill before moving to Port Vale in 1899. The following year he joined West Ham. Grassam scored 4 goals on his debut in a 7-0 victory over Gravesend. By the end of the season Grassam was the club's top scorer with 15 goals. He followed this with 10 goals in 1901-02 and 19 in 1902-03. Grassam moved to Manchester United and also had spells with Celtic and Leyton before rejoining West Ham in 1905. He only scored 3 goals in 1905-06 but he was back on top form in the next two seasons where he formed a good partnership with Harry Stapley. The good form of Danny Shea and Fred Blackburn in 1908-9 meant that Grassam only managed nine games. He left West Ham for a second time in 1910.