The first CD Mosconia was founded in 1945 and dissolved in 1958. The current team was founded in 1961 under the name of Grado Club de Fútbol, used until 1970 when the club changed its denomination to the one used currently.
In 2011 the club was relegated to Primera Regional, sixth tier, its worst result ever. After a serious financial trouble, the supporters helped the club to avoid the dissolution and to come back, years later, to Tercera División.