Aiming at the problem of anti crosswind landing control of carrier based aircraft, a low pass nonsingular terminal sliding mode control (LNTSMC) algorithm is designed to improve the anti crosswind guidance ability of the carrier based aircraft. Firstly, based on $H_\infty$ mixed sensitivity control, the inner loop attitude robust control system is designed, and the lateral carrier landing guidance equation is derived. Then, an integral nonsingular terminal sliding mode surface is designed based on the homogeneous theory, which can meet the design requirements of the low pass sliding mode controller and avoid the control singularity phenomenon. A power exponential reaching law with a boundary layer is proposed to suppress the chattering in sliding mode control, and a non-homogeneous disturbance observer is introduced to improve the robust stability inside the boundary layer. Finally, the finite time stability of the algorithm is proved using the Lyapunov theorem, and the simulation analysis is given. The simulation results show that the guidance algorithm designed in this paper has good anti crosswind performance, and the superiority of the algorithm is verified by comparing with the existing algorithms.