The primary goal of continual learning (CL) task in medical image segmentation field is to solve the "catastrophic forgetting" problem, where the model totally forgets previously learned features when it is extended to new categories (class-level) or tasks (task-level). Due to the privacy protection, the historical data labels are inaccessible. Prevalent continual learning methods primarily focus on generating pseudo-labels for old datasets to force the model to memorize the learned features. However, the incorrect pseudo-labels may corrupt the learned feature and lead to a new problem that the better the model is trained on the old task, the poorer the model performs on the new tasks. To avoid this problem, we propose a network by introducing the data-specific Mixture of Experts (MoE) structure to handle the new tasks or categories, ensuring that the network parameters of previous tasks are unaffected or only minimally impacted. To further overcome the tremendous memory costs caused by introducing additional structures, we propose a Low-Rank strategy which significantly reduces memory cost. We validate our method on both class-level and task-level continual learning challenges. Extensive experiments on multiple datasets show our model outperforms all other methods.