The realization of practical intelligent reflecting surface (IRS)-assisted multi-user communication (IRS-MUC) systems critically depends on the proper beamforming design exploiting accurate channel state information (CSI). However, channel estimation (CE) in IRS-MUC systems requires a significantly large training overhead due to the numerous reflection elements involved in IRS. In this paper, we adopt a deep learning approach to implicitly learn the historical channel features and directly predict the IRS phase shifts for the next time slot to maximize the average achievable sum-rate of an IRS-MUC system taking into account the user mobility. By doing this, only a low-dimension multiple-input single-output (MISO) CE is needed for transmit beamforming design, thus significantly reducing the CE overhead. To this end, a location-aware convolutional long short-term memory network (LA-CLNet) is first developed to facilitate predictive beamforming at IRS, where the convolutional and recurrent units are jointly adopted to exploit both the spatial and temporal features of channels simultaneously. Given the predictive IRS phase shift beamforming, an instantaneous CSI (ICSI)-aware fully-connected neural network (IA-FNN) is then proposed to optimize the transmit beamforming matrix at the access point. Simulation results demonstrate that the sum-rate performance achieved by the proposed method approaches that of the genie-aided scheme with the full perfect ICSI.