With the development and strengthening of interception measures, the traditional penetration methods of high-speed unmanned aerial vehicles (UAVs) are no longer able to meet the penetration requirements in diversified and complex combat scenarios. Due to the advancement of Artificial Intelligence technology in recent years, intelligent penetration methods have gradually become promising solutions. In this paper, a penetration strategy for high-speed UAVs based on improved Deep Reinforcement Learning (DRL) is proposed, in which Long Short-Term Memory (LSTM) networks are incorporated into a classical Soft Actor–Critic (SAC) algorithm. A three-dimensional (3D) planar engagement scenario of a high-speed UAV facing two interceptors with strong maneuverability is constructed. According to the proposed LSTM-SAC approach, the reward function is designed based on the criteria for successful penetration, taking into account energy and flight range constraints. Then, an intelligent penetration strategy is obtained by extensive training, which utilizes the motion states of both sides to make decisions and generate the penetration overload commands for the high-speed UAV. The simulation results show that compared with the classical SAC algorithm, the proposed algorithm has a training efficiency improvement of 75.56% training episode reduction. Meanwhile, the LSTM-SAC approach achieves a successful penetration rate of more than 90% in hypothetical complex scenarios, with a 40% average increase compared with the conventional programmed penetration methods.