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 paper, an adaptive backstepping radial basis function 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 radial basis function 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 unknown uncertainties. The proposed adaptive backstepping radial basis function neural network controller guarantees that tracking errors and radial basis sunction 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. The simulation results show that the adaptive backstepping radial basis function 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 radial basis function neural network has an outstanding capability to approximate unknown nonlinear functions.