Aiming at the problems of traditional 3D RRT* global path planning algorithm, such as large sampling base, large calculation of parent node reselecting, blind node expansion, and unsmooth search path, a target bidirectional 3D RRT* path planning algorithm based on approximate geodesic obstacle avoidance strategy (AGTB-RRT*) is proposed in this paper. Firstly, the approximate median node is set on the connection path of the bidirectional target point, and the random tree is built to extend bidirectional towards the starting point and target point, which effectively improves the search efficiency of the algorithm. The heuristic sampling space is established based on the one leaf hyperboloid, which effectively reduces the sampling base and the calculation of parent node reselecting, and reduces the memory occupation. Secondly, threshold switching is performed on the target point and random points, and the target gravitational potential field is established, which effectively reduces the blindness of node expansion and improves the convergence speed of the algorithm. Thirdly, the triangular mesh envelope is established for the 3D obstacles, and the approximate geodesic method is used to make the nodes quickly detour along the 3D obstacles envelope surface, and then a local obstacle avoidance path with low cost and high speed is planned. Finally, the B-spline curve fitting method is used to optimize the entire generated path to obtain a smooth and optimal feasible path. Simulation results verify the effectiveness and feasibility of the proposed AGTB-RRT* algorithm for path planning in 3D space.