Herman “Junior” Cook (July 22, 1934 – February 3, 1992) was an American hard bop tenor saxophone player.

Cook was born in Pensacola, Florida. After playing with Dizzy Gillespie in 1958, Cook gained some fame for his longtime membership in the Horace Silver Quintet (1958–1964); when Silver left the group in the hands of Blue Mitchell Cook stayed in the quintet for five more years (1964–1969). Later associations included Freddie Hubbard, Elvin Jones, George Coleman, Louis Hayes (1975–1976), Bill Hardman (1979–1989), and the McCoy Tynerbig band.