The aim of this present paper is that of developing a high performance intelligent controller for aero-engines based on deep reinforcement learning, in order to overcome the dependency of expertise and complex parameter tuning procedure for traditional aero-engine control design. In this paper, a deep reinforcement learning algorithm, i.e. twin delayed deep deterministic policy gradient algorithm(TD3), is combined with a traditional proportion integral differential (PID) controller for the shaft speed control of a typical dual-shaft turbofan engine. The combined controller performs self-tuning strategy to achieve performance optimization for the controlled system, without any human intuition and prior expert knowledge behind about the dynamics of the aero-engine. A nonlinear component level model of a dual-shaft turbofan engine is developed for the training and verification procedures of the proposed control algorithm. Simulation results demonstrate that compared with traditional PID controller with time-consuming manual parameter fine-tuning, the proposed intelligent control algorithm gives improved control performance for the aero-engine model with significant reduced tuning time, with no dependence of prior knowledge of the engine dynamics.