The spinning flow of liquid crystalline polymers is numerically calculated using a modified Doi model. The flow dealt with is an axisymmetric spinning flow for the examination of velocity and molecular orientation developments inside a filament and is solved with a finite difference method. The velocity profile varies from a convex profile to a uniform one through a concave one that is peculiar to the liquid crystalline polymers. The distribution of the molecular orientation near the nozzle exit is found to cause the generation of the concave profile. Furthermore, the results of the simulation suggest the requirement of a long spinline for the attainment of a uniform profile of the molecular orientation inside a fiber.