In this paper, we study an intelligent reflecting surface (IRS)-aided wireless secure communication system, where an IRS is deployed to adjust its reflecting elements to secure the communication of multiple legitimate users in the presence of multiple eavesdroppers. Aiming to improve the system secrecy rate, a design problem for jointly optimizing the base station (BS)'s beamforming and the IRS's reflecting beamforming is formulated considering different quality of service (QoS) requirements and time-varying channel conditions. As the system is highly dynamic and complex, and it is challenging to address the non-convex optimization problem, a novel deep reinforcement learning (DRL)-based secure beamforming approach is firstly proposed to achieve the optimal beamforming policy against eavesdroppers in dynamic environments. Furthermore, post-decision state (PDS) and prioritized experience replay (PER) schemes are utilized to enhance the learning efficiency and secrecy performance. Specifically, a modified PDS scheme is presented to trace the channel dynamic and adjust the beamforming policy against channel uncertainty accordingly. Simulation results demonstrate that the proposed deep PDS-PER learning based secure beamforming approach can significantly improve the system secrecy rate and QoS satisfaction probability in IRS-aided secure communication systems.