Unmanned aerial vehicles, especially quadcopters, play key roles in many real-world applications and the related quadcopter autonomous control algorithms have attracted a great deal of attention. In this paper, we address the vision-based autonomous landing problem of a quadcopter on a ground moving target. Firstly, we propose a disturbance observer-based control algorithm, consisting of a nonlinear disturbance observer and robust altitude and attitude controllers. This algorithm is based on the quadcopter dynamics model, and its stability is strictly proved using Lyapunov’s theory. Secondly, we develop an autonomous landing planner which we test for various landing scenarios to deliver improved reliability and accuracy of the landing mission. These theoretical studies are complemented by a numerical feasibility study, before demonstrating the effectiveness of our approach under actual flight conditions with an experimental quadcopter platform.