Following the release of Trapeze's self-titled debut album Trapeze in early 1970, lead vocalist John Jones and keyboardist Terry Rowley left the band, leaving guitarist Mel Galley, bassist Glenn Hughes and drummer Dave Holland to continue as a trio. Four of the seven songs on Medusa were written by Galley and his brother Tom, two were written by Hughes, and one was written by the trio.
Critical reception for Medusa was generally positive. A review published on AllMusic awarded the album four and a half out of five stars, with writer Jason Anderson describing the album as "the finest offering from '70s outfit Trapeze" and "one of the decade's most underappreciated hard rock recordings". Anderson praised Hughes's "soulful vocal delivery" and Galley's "catchy and affective" guitar performance, concluding that "it's a wonder that the record isn't mentioned more when influential albums of this era are discussed".