When a Mars lander is guided to follow a predetermined reference trajectory during the powered descent phase, large tracking errors occur due to strong perturbations caused by enormous external disturbances, such as the Martian atmosphere and wind and dust storms, as well as considerable uncertainties. The tracking performance is determined directly by the accuracy of the system model, especially with regard to nonlinear terms. In this dissertation, an adaptive backstepping radial basis function (RBF) neural network controller is developed for a Mars lander to achieve precise tracking to a reference trajectory during the powered descent phase. The main part of the controller is designed with backstepping, and a RBF neural network with an online adaptive law for the weight vector is used as an auxiliary part to approximate unknown nonlinear functions, including the gravitational force, Coriolis force, centrifugal force, atmospheric drag force, atmospheric lift force, wind force, and large uncertainties. The proposed adaptive backstepping RBF neural network controller guarantees that tracking errors and RBF neural network weight estimation errors eventually converge to the uniformly ultimately bounded values according to the Lyapunov stability theory. Additionally, this study presents an online adaptive law for the weight vector to approximate the unknown nonlinear functions. The simulation results show that the adaptive backstepping RBF neural network controller has an excellent tracking performance in the severe environmental conditions of Mars with strong external disturbances and large variations in uncertainties. Furthermore, this study reveals that the RBF neural network has an outstanding capability to approximate unknown nonlinear functions.