The adaptive cycle engine can adapt to the requirements of aircraft subsonic flight and supersonic flight, and its acceleration process shows strong nonlinearity. The deep reinforcement learning method has strong adaptive learning ability for complex uncertain environments, and is suitable for the Markov decision-making process of adaptive cycle engine acceleration control. This paper proposes an adaptive cycle engine acceleration controller based on deep reinforcement learning method. The deep deterministic strategy gradient algorithm is applied to the continuous control process. Ornstein-uhlenbeck noise is used to explore the noise to match the inertial system of the engine acceleration process. A delay term is introduced to match the engine’s actuator performance. The simulation results show that the controller can fully tap the performance potential of the engine and shorten the acceleration time while ensuring safety.