Deformable image registration plays a crucial role in medical image analysis. Despite various advanced registration models having been proposed, achieving accurate and efficient deformable registration remains challenging. Leveraging the recent outstanding performance of Mamba in computer vision, we introduced a novel model called MCRDP-Net. MCRDP-Net adapted a dual-stream network architecture that combined Mamba blocks and convolutional blocks to simultaneously extract global and local information from fixed and moving images. In the decoding stage, we employed a pyramid network structure to obtain high-resolution deformation fields, achieving efficient and precise registration. The effectiveness of MCRDP-Net was validated on public brain registration datasets, OASIS and IXI. Experimental results demonstrated significant advantages of MCRDP-Net in medical image registration, with DSC, HD95, and ASD reaching 0.815, 8.123, and 0.521 on the OASIS dataset and 0.773, 7.786, and 0.871 on the IXI dataset. In summary, MCRDP-Net demonstrates superior performance in deformable image registration, proving its potential in medical image analysis. It effectively enhances the accuracy and efficiency of registration, providing strong support for subsequent medical research and applications.