Test-time adaptation (TTA) is a special and practical setting in unsupervised domain adaptation, which allows a pre-trained model in a source domain to adapt to unlabeled test data in another target domain. To avoid the computation-intensive backbone fine-tuning process, the zero-shot generalization potentials of the emerging pre-trained vision-language models (e.g., CLIP, CoOp) are leveraged to only tune the run-time prompt for unseen test domains. However, existing solutions have yet to fully exploit the representation capabilities of pre-trained models as they only focus on the entropy-based optimization and the performance is far below the supervised prompt adaptation methods, e.g., CoOp. In this paper, we propose SwapPrompt, a novel framework that can effectively leverage the self-supervised contrastive learning to facilitate the test-time prompt adaptation. SwapPrompt employs a dual prompts paradigm, i.e., an online prompt and a target prompt that averaged from the online prompt to retain historical information. In addition, SwapPrompt applies a swapped prediction mechanism, which takes advantage of the representation capabilities of pre-trained models to enhance the online prompt via contrastive learning. Specifically, we use the online prompt together with an augmented view of the input image to predict the class assignment generated by the target prompt together with an alternative augmented view of the same image. The proposed SwapPrompt can be easily deployed on vision-language models without additional requirement, and experimental results show that it achieves state-of-the-art test-time adaptation performance on ImageNet and nine other datasets. It is also shown that SwapPrompt can even achieve comparable performance with supervised prompt adaptation methods.