<p>Medical image registration plays a crucial role in tumor growth monitoring, radiotherapy planning, and disease diagnosis. Recently, Transformer-based networks have been widely adopted in unsupervised image registration, achieving improved registration accuracy. However, the use of attention mechanisms significantly increases model complexity with substantial computational and memory costs, failing to meet the real-time requirements of medical image registration. To address these challenges, this paper proposes a Hierarchical Pyramid Network with Lipschitz Continuity Constraint and Spatial Recurrent Encoding Module for Medical Image Registration (LHPS-Net). The model employs a hierarchical pyramid architecture that enhances registration performance through Lipschitz continuity constraints and spatial recurrent encoding. Specifically, unlike traditional deep learning-based approaches, LHPS-Net independently extracts features from fixed and moving images and progressively generates deformation fields through hierarchical decoders, which facilitates large-deformation image registration. The spatial recurrent encoding module replaces conventional convolutional blocks, utilizing SLK (Spatial Locally-connected Kernel) to capture contextual information with lower computational cost while effectively focusing on multi-scale features. The LC-Def block incorporates Lipschitz continuity constraints to help achieve diffeomorphic deformation. To validate the performance of our proposed network, we conducted comprehensive comparisons with existing methods on public datasets including IXI, LPBA, and OASIS. Experimental results demonstrate that LHPS-Net achieves superior registration performance under common evaluation metrics.</p>