Can introduce a second cis double bond at the Delta(12) position of fatty acid bound to membranes glycerolipids. This enzyme is involved in chilling tolerance because the phase transition temperature of lipids of cellular membranes depends on the degree of unsaturation of fatty acids of the membrane lipids. (9Z)-octadecenoyl-CoA + 2 Fe(II)-[cytochrome b5] + 2 H(+) + O2 = (9Z,12Z)-octadecadienoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O (9Z)-hexadecenoyl-CoA + 2 Fe(II)-[cytochrome b5] + 2 H(+) + O2 = (9Z,12Z)-hexadecadienoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O Lipid metabolism; polyunsaturated fatty acid biosynthesis. Belongs to the fatty acid desaturase type 1 family.