In this article, a theory analysis of the steady director of nematic polymers in Hele-Shaw flow was given. The Ericksen's Transversely Isotropic Fluid equations are used for modeling the motion of the director. There is a singular point for the steady state of director in expanding Hele-Shaw flows. If the shear rate in the direction perpendicular to the flow plane is larger than a switch value, which is a function of velocity derivatives in the flow plane, the steady director will align with the flow direction; otherwise, it will tend to be perpendicular to the flow direction. Under this result, the Leslie-Ericksen (L-E) theory may explain the widely recognized phenomenon in the molding process of nematic polymers, which is that the molecular chains in the skin regions are largely aligned along the injection direction while the chain orientation in the central core is more or less random.