Spirulina produces $gamma$-linolenic acid (GLA), an important pharmaceutical substance, in a relatively low level compared with fungi and plants, prompting more research to improve its GLA yield. In this study, metabolic flux analysis was applied to determine the cellular metabolic flux distributions in the GLA synthetic pathways of two Spiru/ina strains, wild type BP and a high­GLA producing mutant Z19/2. Simplified pathways involving the GLA synthesis of S. platensis formulated comprise of photosynthesis, gluconeogenesis, the pentose phosphate pathway, the anaplerotic pathway, the tricarboxylic cycle, the GLA synthesis pathway, and the biomass syn­thesis pathway. A stoichiometric model reflecting these pathways contains 17 intermediates and 22 reactions. Three fluxes - the bicarbonate (C-source) uptake rate, the specific growth rate, and the GLA synthesis rate - were measured and the remaining fluxes were calculated using lin­ear optimization. The calculation showed that the flux through the reaction converting acetyl­CoA into malonyl-CoA in the mutant strain was nearly three times higher than that in the wild­type strain. This finding implies that this reaction is rate controlling. This suggestion was sup­ported by experiments, in which the stimulating factors for this reaction $(NADPH;and;MgCl_{2})$ were added into the culture medium, resulting in an increased GLA-synthesis rate in the wild type strain.