Abstract: Autonomous outdoor robots have been witnessed in recent years. The outdoor navigation is more difficult than the indoor one because the outdoor environment is more complicated. Various methods for outdoor navigation were proposed. Vision-based methods are vulnerable to weather, road marker-based methods lack flexibility and machine learning-based methods are unable to cope with the complex outdoor environments. A navigation method is proposed in this paper, which includes a real-time local grid map constructer, road direction-based trajectory planner, and model predictive control-based tracking controller. During the navigation task, the point cloud of the surrounding environment is obtained through a 16 thread radar, and the local grid map is constructed in real time. The mission goal is transformed to the robot coordinates, then the improved A-star algorithm based on the road direction is used to search the local obstacle avoidance path. Finally, a differential robot model predictive controller is designed to track the trajectory. Both simulation and experimental results are presented and discussed. It is revealed in the simulation tests that the designed planner can ensure collision avoidance with fewer turns and the designed motion controller has good tracking performance, which helps to reduce total mission execution time. It is shown in the outdoor experiment that the navigation method drives the robot to preselected mission point in turn with a stable motion. The distance between the robot and the obstacle is more than 1 m in the process of obstacle avoidance. Furthermore, there is no need to build a map in advance, the proposed method is more applicable and efficient in various outdoor environments.