Utilizing the geometric properties that geodesic is the shortest path between two points in metric space, a method for trajectory planning of mobile robots based on geodesic was proposed. The Riemannian metric of the square of the arc length of the mobile robot’〖KG-*3〗s trajectory was constructed with the left and right wheel angles of the two-wheel differential drive robot as a parameter, and the geodesic determined by the Riemann metric was used as the optimal trajectory of the robot.The Christoffel symbol of the geodesic equation was solved according to the Riemannian metric, then the geodesic equation representing the shortest path was solved, the wheel rotation angle and angular velocity were directly obtained, and the optimal geodesic trajectory was generated.