In recent years, lower limb exoskeletons (LLEs) have attracted considerable interest for the walking assistance of paraplegic patients. As the wearable robots, gait planning is a critical issue for LLEs, especially adaptive gait pattern generation for different terrains such as slopes and stairs. This paper proposes an adaptive human-like gait planning approach (AHGP) for the stair climbing of LLEs, which realizes the generation of adaptive and human-like gait trajectories for varying stair heights. The AHGP divides one step on the stair into five sub-phases, and in each phase, the AHGP employs the artificial potential field to generate the optimal ankle positions to avoid the collision with each step on the stair. To obtain human-like gait patterns, Kernelized Movement Primitives were employed to learn and generate gait trajectories, i.e., the hip and the ankle positions for each leg in the Cartesian space. After learning from the demonstrated trajectories collected from the healthy subjects, the human-like gait trajectories passing through the generated optimal ankle positions can be reproduced to adapt to stairs with different heights. The proposed approach has been tested with the exoskeleton robot simulation model, and the experimental results indicate that the AHGP can generate the appropriate gait trajectories for LLEs to walk over varying stairs.