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Human beings can quickly adapt to environmental changes by leveraging learning experience. However, the poor ability of adapting to dynamic environments remains a major challenge for AI models. To better understand this issue, we study the problem of continual domain adaptation, where the model is presented with a labeled source domain and a sequence of unlabeled target domains. There are two major obstacles in this problem: domain shifts and catastrophic forgetting. In this work, we propose Gradient Regularized Contrastive Learning to solve the above obstacles. At the core of our method, gradient regularization plays two key roles: (1) enforces the gradient of contrastive loss not to increase the supervised training loss on the source domain, which maintains the discriminative power of learned features; (2) regularizes the gradient update on the new domain not to increase the classification loss on the old target domains, which enables the model to adapt to an in-coming target domain while preserving the performance of previously observed domains. Hence our method can jointly learn both semantically discriminative and domain-invariant features with labeled source domain and unlabeled target domains. The experiments on Digits, DomainNet and Office-Caltech benchmarks demonstrate the strong performance of our approach when compared to the state-of-the-art.