In this paper, we study an intelligent reflecting surface (IRS)-aided wireless secure communication system for physical layer security, where an IRS is deployed to adjust its surface reflecting elements to guarantee secure 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 given the different quality of service (QoS) requirements and time-varying channel condition. 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, PDS is capable of tracing the environment dynamic characteristics and adjust the beamforming policy 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.