Development of the strain and the fermentation process of Hansenula polymorpha was implemented for the production of ${gamma}$-linolenic acid ($GLA,;C18:3{Delta}^{6,9,12}$), an n-6 polyunsaturated fatty acid (PUFA) that has been reported to possess a number of health benefits. The mutated ${Delta}^6$-desaturase (S213A) gene of Mucor rouxii was expressed in H. polymorpha under the control of the methanol oxidase (MOX) promoter. Without the utilization of methanol, a high-cell-density culture of the yeast recombinant carrying the ${Delta}^6$-desaturase gene was then achieved by fed-batch fermentation under glycerol-limited conditions. As a result, high levels of the ${Delta}^6$-desaturated products, octadecadienoic acid ($C18:2{Delta}^{6,9}$), GLA, and stearidonic acid ($C18:4{Delta}^{6,9,12,15}$), were accumulated under the derepression conditions. The GLA production was also optimized by adjusting the specific growth rate. The results show that the specific growth rate affected both the lipid content and the fatty acid composition of the GLA-producing recombinant. Among the various specific growth rates tested, the highest GLA concentration of 697 mg/l was obtained in the culture with a specific growth rate of 0.08 /h. Interestingly, the fatty acid profile of the yeast recombinant bearing the Mucor ${Delta}^6$-desaturase gene was similar to that of blackcurrant oil, with both containing similar proportions of n-3 and n-6 essential fatty acids.