Path planning is the most critical step in the search area coverage, which plays a vital role in many search tasks like regional surveillance, search, and rescue, hazard monitoring, etc. UAVs equipped with SAR sensors (SAR-UAV) are usually adopted in search area coverage tasks for their great superiority over optical sensors w.r.t the ability to "see" through the darkness, clouds, and rain. The traditional coverage path planning methods can hardly derive optimal plans or respond to environmental changes in time. We proposed a coverage path planning algorithm based on DRL to handle the search area coverage problem for SAR-UAV in this paper. We first modeled the imaging process of SAR-UAV, and we then designed the RL algorithm's action space, reward function, etc. Finally, we enabled the SAR-UAV to cover every point in the task area by controlling the actions of the SAR-UAV based on deep reinforcement learning. The experimental results show that the proposed method can complete the search area coverage tasks of various sizes, reduce the risk of exposure and minimize power loss, which demonstrates the effectiveness of the proposed method on search area coverage.