Projecting images onto non-planar surfaces inevitably introduces geometric distortions that degrade visual quality. Traditional correction methods often require tedious manual calibration or structured light sequences to establish pixel-wise correspondences. In this paper, we develop the Curved Surface Projection Rectification Network (CSPR-Net), a self-supervised deep learning framework for automated distortion correction. Our approach employs dual coordinate-based neural networks to learn the bi-directional mapping between the projector and camera spaces. By enforcing a robust cycle-consistency constraint, CSPR-Net autonomously resolves complex geometric transformations without requiring ground-truth deformation fields. Furthermore, a gradient-based loss function is introduced to mitigate the impact of complex ambient light interference and accurately capture high-frequency geometric variations. Quantitative evaluations in physical experimental scenarios demonstrate that CSPR-Net achieves a 20.7% improvement in end-to-end fidelity (SSIM) and outperforms the polynomial baseline by 3.8% and 5.4% in forward and inverse mapping in terms of SSIM respectively, effectively generating high-precision pre-warped images for seamless projection.