Grammos played as right forward or right midfielder. He was a mainstay for Panathinaikos for the next 10 years and was a member of the team that played at 1971 European Cup Final in Wembley Stadium. Later in his career, he played for Olympiakos, becoming one of the few players that made the cross-over between the two "eternal enemies". Grammos made a total of 215 appearances in the Alpha Ethniki.