In allusion to the trajectory tracking process of interception against hypersonic targets in near space, a novel tracking guidance law based on linear quadratic regulator theory and Gauss pseudospectral method was designed. In order to track the nominal trajectory accurately, the linear quadratic tracking problem was considered, while the sufficient and necessary conditions for optimal solutions were deduced with the optimal control theory to acquire the expression of linear state feedback control variables. Based on Gauss pseudospectral method, the time-varying difference matrixes and coefficient matrixes were calculated by using the information of the nominal trajectory on the Legendre-Gauss points to obtain the state disturbances feedback control law. Simulation results show that, compared with the method by solving Riccati equation, this method can obtain the feedback control variables with high accuracy and computation efficiency by less nodes and satisfy the requirement of on-line implementation.