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 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, a novel deep reinforcement learning (DRL)-based secure beamforming approach is firstly proposed to achieve the optimal beamforming policy against eavesdroppers in dynamic environments. Simulation results demonstrate that the proposed deep learning based secure beamforming approach can significantly improve the system secrecy performance compared with other approaches.