This paper studies a secure satellite-terrestrial communication system assisted by a hybrid intelligent reflecting surface (IRS). The hybrid IRS, which composes of active and passive reflecting elements, is deployed to enhance the secure communication from the satellite to multiple users against multiple eavesdroppers. A joint design optimization problem for the satellite beamforming and the hybrid IRS interaction is formulated to maximize the system worst-case secrecy rate under time-varying channel conditions. With high system dynamic and complexity, deep reinforcement learning (DRL) is employed to solve the non-convex optimization problem. We propose a fast DRL algorithm, namely deep PDS-DPG, to obtain the robust secure beamforming design for satellite and hybrid IRS. Numerical results show a better learning efficiency of the proposed algorithm as to the state-of-the-art deep deterministic policy gradient (DDPG) algorithm with comparable system secrecy performance.