An optimized model KUNet based on Kolmogorov-Arnold network (KAN) and convolutional KAN (CKAN) was proposed to enhance the performance of the UNet model in order to address the limitation of the UNet model in complex feature extraction and generalization capability for medical image segmentation task. Traditional convolutional layer was replaced with CKAN, KAN feature enhancement module was introduced, and skip connection was optimized. Then the diversity and accuracy of feature extraction were improved while preserving structural information by incorporating an adaptive basis function learning mechanism. Comparative experiments were conducted against the UNet baseline model, nnUNet model and Swin-UNet model on four different multimodal datasets: LiTS, CORN, DRIVE and Lungs. Results showed that the average maximum absolute performance gap (MAPG) between the UNet baseline model and the KUNet model across the four datasets were 0.679 9 and 0.620 3 for Dice coefficient and IoU coefficient, respectively, and the KUNet model achieved average improvement metrics of 0.3213 and 0.2625 compared with the optimal or suboptimal model across the four datasets. The KUNet model was utilized to effectively extract more feature within short training cycle and improve the accuracy of image segmentation.