He became famous with the thriller film El expreso de Andalucía (The Andalusian express) (1956) under the direction of Francisco Rovira Beleta.
[1] He made two films directed by Mauel Mur Otis: Fedra (1956), an adaptation of the classical play, and the melodrama El batallón de las sombras (1957).
The same year he starred in Rapsodia de sangre (1957) a film directed by Antonio Isasi-Isasmendi about the Hungarian Revolution of 1956.
[3] In the following years Parra starred in the musical Nobleza baturra (Aragonese nobility) (1965) and he mixed his work in the theater, where he formed his own company, with edgier parts in films like: Varietés (Variety) (1971) under the direction of Juan Antonio Bardem.
In La Semana del asesino, he played a working class serial killer who put his victims through the grinder at a meat factory.