(9Z,12Z)-octadecadienoyl-CoA + 2 Fe(II)-[cytochrome b5] + 2 H(+) + O2 = (6Z,9Z,12Z)-octadecatrienoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O (9Z,12Z,15Z)-octadecatrienoyl-CoA + 2 Fe(II)-[cytochrome b5] + 2 H(+) + O2 = (6Z,9Z,12Z,15Z)-octadecatetraenoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O Belongs to the fatty acid desaturase type 1 family.