Quadcopters have been studied for decades thanks to their maneuverability and capability of operating in a variety of circumstances. However, quadcopters suffer from dynamical nonlinearity, actuator saturation, as well as sensor noise that make it challenging and time consuming to obtain accurate dynamic models and achieve satisfactory control performance. Fortunately, deep reinforcement learning came and has shown significant potential in system modelling and control of autonomous multirotor aerial vehicles, with recent advancements in deployment, performance enhancement, and generalization. In this paper, an end-to-end deep reinforcement learning-based controller for quadcopters is proposed that is secure for real-world implementation, data-efficient, and free of human gain adjustments. First, a novel actor-critic-based architecture is designed to map the robot states directly to the motor outputs. Then, a quadcopter dynamics-based simulator was devised to facilitate the training of the controller policy. Finally, the trained policy is deployed on a real Crazyflie nano quadrotor platform, without any additional fine-tuning process. Experimental results show that the quadcopter exhibits satisfactory performance as it tracks a given complicated trajectory, which demonstrates the effectiveness and feasibility of the proposed method and signifies its capability in filling the simulation-to-reality gap.