In this article, we study the ground moving target tracking problem for a fixed-wing unmanned aerial vehicle equipped with a radar. This problem is formulated in a partially observable Markov process framework, which contains the following two parts: in the first part, the unmanned aerial vehicle utilizes the measurements from its radar and employs a Kalman filter to estimate the target’s real-time location; in the second part, the unmanned aerial vehicle optimizes its trajectory in a real-time manner so that the radar’s measurements can include more useful information. To solve the trajectory optimization problem, we proposed an information geometry-based partially observable Markov decision process method. Specifically, the cumulative amount of information in the observation is represented by Fisher information of information geometry, and acts as the criterion of the partially observable Markov decision process problem. Furthermore, to guarantee the real-time performance, an important trade-off between the optimality and computation cost is made by an approximate receding horizon approach. Finally, simulation results corroborate the accuracy and time-efficiency of our proposed method and also show our advantage in computation time compared to existing methods.