In order to produce ${gamma}-linolenic$ acid by Mucor sp. KCTC 8405P. the fungus was cultivated in fed-batch culture with two phases. i.e., growth in yeast-like form and induction to hyphal growth by pH shift of the culture medium during cultivation. The synchronous growth of the fungus into the appropriate sizes was important for the high density cell culture of this dimorphic fungus. Dissolved oxygen concentration in the medium did not affect degree of unsaturation of fatty acids and ${gamma}-linolenic$ acid content. Under the culture conditions applied in this experiment. the fungus was found to produce 100 g/l dry mycelia containing 40% of the lipids, where ${gamma}-linolenic$ acid comprised about 9% of the total extractable fatty acids.