Cremona was founded in Schönbach in Czechoslovakia in 1922 as a stringed instrument manufacturer. Following World War II in 1946, as Schönbach was renamed Luby, Cremona became a cooperative of 40 instrument makers. The Communist government nationalised the Cremona cooperative in 1950 and it became a state owned enterprise, with a main plant and warehouse divided into many small workshops. Cremona made classical and acoustic guitars as well as electric guitars and basses, and orchestral stringed instruments.

In 1992 Cremona was privatised and renamed Strunal Schönbach.