Driving in an off-road environment is challenging for autonomous vehicles due to the complex and varied terrain. To ensure stable and efficient travel, the vehicle requires consideration and balancing of environmental factors, such as undulations, roughness, and obstacles, to generate optimal trajectories that can adapt to changing scenarios. However, traditional motion planners often utilize a fixed cost function for trajectory optimization, making it difficult to adapt to different driving strategies in challenging irregular terrains and uncommon scenarios. To address these issues, we propose an adaptive motion planner based on human-like cognition and cost evaluation for off-road driving. First, we construct a multi-layer map describing different features of off-road terrains, including terrain elevation, roughness, obstacle, and artificial potential field map. Subsequently, we employ a CNN-LSTM network to learn the trajectories planned by human drivers in various off-road scenarios. Then, based on human-like generated trajectories in different environments, we design a primitive-based trajectory planner that aims to mimic human trajectories and cost weight selection, generating trajectories that are consistent with the dynamics of off-road vehicles. Finally, we compute optimal cost weights and select and extend behavioral primitives to generate highly adaptive, stable, and efficient trajectories. We validate the effectiveness of the proposed method through experiments in a desert off-road environment with complex terrain and varying road conditions. The experimental results show that the proposed human-like motion planner has excellent adaptability to different off-road conditions. It shows real-time operation, greater stability, and more human-like planning ability in diverse and challenging scenarios.