Previous research on code intelligence usually trains a deep learning model on a fixed dataset in an offline manner. However, in real-world scenarios, new code repositories emerge incessantly, and the carried new knowledge is beneficial for providing up-to-date code intelligence service to developers. In this paper, we aim at the following problem: How to enable code intelligence models to continually learn from ever-increasing data? One major challenge here is catastrophic forgetting, meaning that the model can easily forget knowledge learned from previous datasets when learning from the new dataset. To tackle this challenge, we propose REPEAT, a novel method for continual learning of code intelligence models. Specifically, REPEAT addresses the catastrophic forgetting problem with representative exemplars replay and adaptive parameter regularization. The representative exemplars replay component selects informative and diverse exemplars in each dataset and uses them to retrain model periodically. The adaptive parameter regularization component recognizes important parameters in the model and adaptively penalizes their changes to preserve the knowledge learned before. We evaluate the proposed approach on three code intelligence tasks including code summarization, software vulnerability detection, and code clone detection. Extensive experiments demonstrate that REPEAT consistently outperforms baseline methods on all tasks. For example, REPEAT improves conventional fine-tuning method by 5.9%, 20.1%, and 2.0% on code summarization, vulnerability detection and clone detection, respectively.