Unmanned combat aerial vehicle (UCAV) trajectory planning to avoid radar detection threats is a complicated optimization problem that has been widely studied. The rapid changes in Radar Cross Sections (RCSs), the unknown cruise trajectory of airborne radar, and the uncertain distribution of radars exacerbate the complexity of this problem. In this paper, we propose a novel UCAV trajectory planning method based on deep reinforcement learning (DRL) technology to overcome the adverse impacts caused by the dynamics and randomness of environments. A predictive control model is constructed to describe the dynamic characteristics of the UCAV trajectory planning problem in detail. To improve the UCAV’s predictive ability, we propose a memory-enhanced twin delayed deep deterministic policy gradient (ME-TD3) algorithm that uses an attention mechanism to effectively extract environmental patterns from historical information. The simulation results show that the proposed method can successfully train UCAVs to carry out trajectory planning tasks in dynamic and unknown environments. Furthermore, the ME-TD3 algorithm outperforms other classical DRL algorithms in UCAV trajectory planning, exhibiting superior performance and adaptability.