Medical image segmentation is essential for identifying lesion regions and diagnosing disease. Convolutional neural networks (CNNs) and transformer-based models often struggle to effectively capture both local details and global contextual features in medical images, leading to a decline in segmentation performance. To address this problem, a novel medical image segmentation model, KMUNet, is proposed by integrating Kolmogorov-Arnold networks (KAN) and Mamba based on the traditional U-shape architecture. This model employs a CNN-based encoder to extract local features and integrates a State Space Model-based Mamba module in the decoder to capture long-range dependencies. Initially, a global downsampling module, called KAN-PatchEmbed is presented. This module differs from traditional convolutional operations in utilizing an interval sampling strategy to alleviate the loss of feature information and KAN to reduce computational complexity, respectively. Furthermore, the Kolmogorov-Arnold Spatial-Channel Attention module is designed for skip connections, where KAN is employed to allocate the weight of the current channel by aggregating features across all stages. Finally, the proposed model was evaluated on three publicly available datasets. Experimental results reveal that KMUNet outperforms other models in segmentation tasks and produces more visually appealing segmentation results. Our code is available at https://github.com/zhang-hongsheng/KMUNet .