Continual learning aims to enable a model to incrementally learn knowledge from sequentially arrived data. Previous works adopt the conventional classification architecture, which consists of a feature extractor and a classifier. The feature extractor is shared across sequentially arrived tasks or classes, but one specific group of weights of the classifier corresponding to one new class should be incrementally expanded. Consequently, the parameters of a continual learner gradually increase. Moreover, as the classifier contains all historical arrived classes, a certain size of the memory is usually required to store rehearsal data to mitigate classifier bias and catastrophic forgetting. In this paper, we propose a non-incremental learner, named AttriCLIP, to incrementally extract knowledge of new classes or tasks. Specifically, AttriCLIP is built upon the pre-trained visual-language model CLIP. Its image encoder and text encoder are fixed to extract features from both images and text prompts. Each text prompt consists of a category name and a fixed number of learnable parameters which are selected from our designed attribute bank and serve as attributes. As we compute the visual and textual similarity for classification, AttriCLIP is a non-incremental learner. The attribute prompts, which encode the common knowledge useful for classification, can effectively mitigate the catastrophic forgetting and avoid constructing a replay memory. We empirically evaluate our AttriCLIP and compare it with CLIP-based and previous state-of-the-art continual learning methods in realistic settings with domain-shift and long-sequence learning. The results show that our method performs favorably against previous state-of-the-arts.