Abstract Background The use of MRI‐guided radiation therapy (MRIgRT) has shown considerable advantages. However, the acquisition of electron density information still relies on Computed tomography (CT) images. In the context of medical image synthesis, achieving high global and local accuracy, as well as efficient synthetic CT (sCT) generation, remains a key challenge. Purpose This study aims to improve the accuracy of sCT image generation from MRI by introducing a novel deep learning model that leverages global context and local detail, with a minimal increase in model complexity. Methods In this study, we propose a novel generative adversarial network based on Mamba block and Residual Constraint (RC) strategy, namely RC‐MambaGAN, which achieves a significant improvement in accuracy with only a minimal increase in computation time required for sCT generation. Specifically, we integrate Mamba block into the generator to enhance the model's ability to capture long‐range contextual information, while preserving the precision of local features and maintaining the global structure of the image. The RC strategy improves the alignment between sCT and real CT by minimizing residuals. The model was validated on multi‐center datasets that included both tumor and pelvic‐region data. Furthermore, the dosimetric accuracy of the generated sCT images was evaluated to assess their clinical applicability. Results RC‐MambaGAN achieved high performance with mean absolute error (MAE) of 37.094 ± 8.761 HU, peak signal‐to‐noise ratio (PSNR) of 28.424 ± 1.145 dB, structural similarity index measure (SSIM) of 0.947 ± 0.004, and Mutual Information (MI) of 1.426 ± 0.012. External validation demonstrated that RC‐MambaGAN outperformed existing state‐of‐the‐art methods in both image quality and quantitative accuracy, even for structures visible in MRI but not in CT images. Conclusions The proposed RC‐MambaGAN markedly improves the image quality and anatomical accuracy of sCT images derived from MRI, thereby advancing the feasibility of MRI‐only radiotherapy workflows.