As a next-generation automotive display technology, Augmented Reality Head-Up Display (AR-HUD) has demonstrated immense potential in reshaping driving safety and enhancing the human–computer interaction experience. To address the challenges of barrel distortion and perspective distortion inherent in HUD systems, we propose a joint-learning-based dual-path pre-correction method. This approach employs a shared encoder to extract image features, which are then decoupled into two parallel branches: a classification branch and a distortion flow prediction branch. Building upon this architecture, a model-fitting method is introduced to estimate the distortion model parameters in the parameter space using the predicted distortion types and flows, thereby reconstructing a refined distortion flow. Finally, image rectification is achieved through a resampling method. On the ARHDD dataset, the proposed method achieves a PSNR of 24.617 dB (barrel) and 25.062 dB (perspective), an SSIM of 0.845 and 0.873, and an NRMSE of 0.163 and 0.157, respectively. On the Places 365 dataset, it achieves a PSNR of 23.914 dB (barrel) and 21.870 dB (perspective), an SSIM of 0.812 and 0.748, and an NRMSE of 0.174 and 0.211, respectively. Both quantitative and qualitative comparative experiments against other state-of-the-art methods demonstrate that the proposed approach achieves superior correction performance for both types of distortion. Finally, the simulation verification of the HUD system proved that this correction method demonstrated excellent potential, but further verification is still needed in a real or semi-real environment.