In this paper, we present the Multi-Center Privacy-Preserving Network (MP-Net), a novel framework designed for secure medical image segmentation in multi-center collaborations. Our methodology offers a new approach to multi-center collaborative learning, capable of reducing the volume of data transmission and enhancing data privacy protection. Unlike federated learning, which requires the transmission of model data between the central server and local servers in each round, our method only necessitates a single transfer of encrypted data. The proposed MP-Net comprises a three-layer model, consisting of encryption, segmentation, and decryption networks. We encrypt the image data into ciphertext using an encryption network and introduce an improved U-Net for image ciphertext segmentation. Finally, the segmentation mask is obtained through a decryption network. This architecture enables ciphertext-based image segmentation through computable image encryption. We evaluate the effectiveness of our approach on three datasets, including two cardiac MRI datasets and a CTPA dataset. Our results demonstrate that the MP-Net can securely utilize data from multiple centers to establish a more robust and information-rich segmentation model.