In this letter, a wideband hybrid precoding network (WHPC-Net) based on deep learning is designed for Terahertz (THz) massive multiple input multiple output (MIMO) system in the face of beam squint. Firstly, the channel state information (CSI) is preprocessed by calculating the mean channel covariance matrix (MCCM). Next, the analog precoder can be calculated based on the analog precoding sub-network (APC-Net) using the information of the MCCM. Finally, the digital precoder will be obtained with the aid of the digital precoding subnetwork (DPC-Net), employing the related outputs of the APC-Net and the MCCM. Simulation results show that the proposed WHPC-Net is more robust to the beam squint over the existing traditional hybrid precoders. For the case of imperfect CSI, the proposed WHPC-Net even is capable of achieving a higher sum rate than the full-digital precoder based on singular value decomposition.