Polyacrylonitrile (PAN) is widely used as a raw material for the production of high-modulus carbon fibers, the internal structure of which is directly affected by the spinning of the precursor. Although PAN fibers have been studied for a long time, the formation of their internal structure has not been sufficiently investigated theoretically. This is due to the large number of stages in the process and the parameters controlling them. In this study, we present a mesoscale model describing the evolution of nascent PAN fibers during the coagulation. It is constructed within the framework of a mesoscale dynamic density functional theory. We use the model to study the influence of a combined solvent of dimethyl sulfoxide (DMSO, a good solvent) and water (a non-solvent) on the microstructure of the fibers. A porous structure of PAN is formed as a result of the microphase separation of the polymer and the residual combined solvent at a high water content in the system. The model shows that one of the possible ways to obtain the homogeneous fiber structure is to slow down the coagulation by increasing the amount of good solvent in the system. This result is in agreement with the existing experimental data and confirms the efficiency of the presented model.