Conventional wheeled or tracked robots are unable to traverse rough, uneven, or steep terrain. A multi-legged robot that has grippers at the tips of each leg is capable of grasping irregularities in the terrain, allowing for free climbing motion through a variety of challenging environments. To execute safe and reliable free-climbing locomotion, the motion of the robot should be planned in consideration of three aspects: optimal selection of gripping points along the path to the goal, tumble stability of the robot including the performance of the gripper, and feasibility of motion on the basis of kinematics. In this paper, we propose a method to satisfy these three conditions and verify the validity of the proposed method with a free-climbing robot walking simulation on inclined terrain with randomly distributed discrete grippable points.