Unmanned aerial vehicles (UAVs), due to their affordability and flexibility, are extensively utilized in target search tasks. However, the complexity and scale of search task search scenarios pose challenges for multi-UAV cooperative search of moving targets. This paper establishes a system model for multi-UAV cooperative search of moving targets to address these challenges. At the same time, the detection performance of the sensor varies with the altitude of the UAV, which is usually ignored in previous studies. A new target probability map update method, based on a revisit time compensation mechanism, is proposed to enhance the UAVs’ ability to capture moving targets. Subsequently, a height-hierarchical adaptive multi-agent deep reinforcement learning algorithm (HHARL) is introduced, allowing UAV swarms to adapt to sensor performance changes and environmental conditions, while also developing an optimized and dynamic search strategy. Finally, a series of experimental results verify the effectiveness of the proposed HHARL algorithm.