Głownia started his senior career with Lechia Gdańsk in 1969, making his debut in the team on 12 October 1969 in a 8–0 win against Gwardia Koszalin.[1] This proved to be his only appearance during his first spell with Lechia, joining Flota Gdynia the season after. While at Flota, the team were involved in a friendly with Widzew Łódź who expressed an interest in Głownia after the match,[2] however Głownia stated that the only club he wished to play for was with Lechia, a situation that was realised in 1972 when he returned to the club. During his second spell with Lechia, he played 8 seasons in the II liga, making a total of 204 appearances in the league during this time. In all competitions over his two spells with Lechia, Głownia made 217 appearances and scored 28 goals.[3] In 1980, Głownia was given the chance to play in the I liga with Arka Gdynia. This was his only season with Arka, making nine appearances and scoring once in Poland's top division.[4] At the end of the 1980–81 season, he emigrated to the United States, where he played for SC Vistula Garfield until 1983. At the end of his playing career, Głownia became a newsagent.[5] He died on 22 September 2024, at the age of 72.[6]