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The automotive augmented reality head-up display (AR-HUD) system projects critical driving information directly into the driver’s line of sight, enhancing driving safety, user experience, and navigation efficiency. However, due to the intrinsic asymmetry of vehicle windshields, existing optical configurations are difficult to use as effective design starting points. The asymmetric transmission region of the windshield causes the AR-HUD optical system to deviate significantly from the YOZ plane, increasing the complexity of system design and optimization. To address these challenges, this paper proposes an automated design method for automotive AR-HUD optical systems. Given the windshield geometry and system design specifications, a normal-guided iterative construction method is first employed to generate a high-performance initial optical structure with low distortion. Subsequently, differentiable ray tracing combined with optimization algorithms is employed to further improve system performance. Based on the proposed method, an AR-HUD optical system with a 130 mm × 50 mm eye-box and a 13° × 4° field of view was designed. The design results indicate that the maximum optical distortion is 0.51%. At five sampled eye positions within the eye-box, the MTF exceeds 0.5 at the spatial frequency of 6 lp/mm, and the dynamic distortion remains below 5.36 ′. Finally, a complete experimental prototype was established, and the experimental results verified the feasibility and effectiveness of the proposed automated design method.