He played for the Boston Bruins, Toronto Maple Leafs, and New York Rangers of the National Hockey League between 1956 and 1969.

Simmons was called up by the Boston Bruins from the Springfield Indians of the minor American Hockey League in order to replace an ailing Terry Sawchuk who had left the Bruins in mid-season of 1957.

He then spent 3 seasons partnering with veteran Harry Lumley as an effective netminding duo in Boston.

Simmons was the second goaltender to adopt the face mask, after Jacques Plante introduced it in 1959.

Later, Simmons would back up Johnny Bower in Toronto in the early 1960s and was instrumental in the Leafs winning the Stanley Cup in 1962.