Electric airplanes have attracted a great deal of attentions because of their strategic commercial values and low emissions. One of the essentials for efficient control and management of hybrid electric propulsion aircraft is a well-designed energy management strategy (EMS). A new EMS approach based on deep learning is introduced in this study to realize thrust distribution and power distribution, consequently lowering aircraft fuel consumption. A model of hybrid electric propulsion power system including turbine engines and lithium-ion battery pack is constructed to act as an application environment. An intelligent energy management strategy based on deep reinforcement learning (DRL) is then proposed in this paper. Two DRL agents based on twin delayed deep deterministic policy gradient (TD3) are combined in the hierarchical framework. The multi-agents are trained to handle the energy management problem in this paper. In a finite period of time, the training process is accomplished. After training, the simulation result of the test shows that this DRL-based EMS reduces the equivalent fuel consumption by 2.2% compared with that using the existing method, and preserves 99.9% of the battery state of health (SOH). The battery pack's state of charge (SOC) regresses precisely to the reference value at the end. Particularly, the proposed EMS is able to work properly for different flight profiles and various initial SOCs. The results of this paper provide preliminary supports for the feasibility and superiority of deep reinforcement learning applied to the energy management strategy of series hybrid electric aircraft.