Stearoyl-CoA desaturase that utilizes O(2) and electrons from reduced cytochrome b5 to introduce the first double bond into saturated fatty acyl-CoA substrates. Catalyzes the insertion of a cis double bond at the delta-9 position into fatty acyl-CoA substrates including palmitoyl-CoA and stearoyl-CoA. Gives rise to a mixture of 16:1 and 18:1 unsaturated fatty acids. Involved in neuronal cell proliferation and differentiation through down-regulation of EGFR/AKT/MAPK and Wnt signaling pathways. 2 Fe(II)-[cytochrome b5] + 2 H(+) + O2 + octadecanoyl-CoA = (9Z)-octadecenoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O 2 Fe(II)-[cytochrome b5] + 2 H(+) + hexadecanoyl-CoA + O2 = (9Z)-hexadecenoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O Expected to bind 2 Fe(2+) ions per subunit. May self-associate and form homodimers. Detected in brain. The histidine box domains are involved in binding the catalytic metal ions. This protein has no ortholog in rodents. Belongs to the fatty acid desaturase type 1 family.