In the process of proving the existence of solitary wave solutions for one-dimensional nematic liquid crystal model equations in W^{1, 2}(-∞, +∞), the key point is to prove that the relevant functional is compact.Therefore, firstly, using the method of concentrated-compactness principle in the critical points theory, two bad cases:dichotomy and vanishing were eliminated, and prove the compactness of the minimizing sequences was proved.Then, the existence of solitary wave solutions for one-dimensional nematic liquid crystal model equations was obtained by using the extremum principle.