In order to plan the robot path in 3D space efficiently, a modified Rapidly-exploring Random Trees based on heuristic probability bias-goal (PBG-RRT) is proposed. The algorithm combines heuristic probabilistic and bias-goal factor, which can get convergence quickly and avoid falling into a local minimum. Firstly, PBG-RRT is used to plan a path. After obtaining path points, path points are rarefied by the Douglas-Peucker algorithm while maintaining the original path characteristics. Then, a smooth trajectory suitable for the manipulator end effector is generated by Non-uniform B-spline interpolation. Finally, the effector is moving along the trajectory by inverse kinematics solving angle of joint. The above is a set of motion planning for the manipulator. Generally, 3D space obstacle avoidance simulation experiments show that the search efficiency of PBG-RRT is increased by 217%, while search time is dropped by 168% compared with P-RRT (Heuristic Probability RRT). After rarefying, the situation where the path oscillated around the obstacle is corrected effectively. And a smooth trajectory is fitted by spline interpolation. Ultimately, PBG-RRT is verified on the ROS (Robot Operating System) with the Robot-Anno manipulator. The results reveal that the validity and reliability of PBG-RRT are proofed in obstacle avoidance planning.