A mathematical model was proposed to simulate the effect of bath concentration on coagulation kinetics at the early stage of wet spinning for the poly(acrylonitrile-co-vinyl acetate)/dimethylsulfoxide (DMSO)/water system. The dependence of critical precipitation time, components concentration distribution, and the radius of nascent fibers on the concentration of DMSO in the DMSO/water coagulation bath were estimated by solving the model equation numerically. The experimental results indicated the model was suitable to simulate the dynamic features of the early stage of the coagulation process. The critical precipitation time was found to increase with bath concentration. The mode of phase separation was changed from instantaneous demixing to delayed demixing as DMSO bath concentration increased. The simulation results showed that bath concentration influenced the phase separation path which determined the polymer concentration distribution in the spinning solution. As a result, nascent fibers with different structures would form in wet spinning and a radial homogeneous structure would be obtained when the DMSO bath concentration increased to some extent.