This ability to learn consecutive tasks without forgetting how to perform previously trained problems is essential for developing an online dialogue system. This paper proposes an effective continual learning method for the task-oriented dialogue system with iterative network pruning, expanding, and masking (TPEM), which preserves performance on previously encountered tasks while accelerating learning progress on subsequent tasks. Specifically, TPEM (i) leverages network pruning to keep the knowledge for old tasks, (ii) adopts network expanding to create free weights for new tasks, and (iii) introduces task-specific network masking to alleviate the negative impact of fixed weights of old tasks on new tasks. We conduct extensive experiments on seven different tasks from three benchmark datasets and show empirically that TPEM leads to significantly improved results over the strong competitors.