This paper proposes Text mAtching based SequenTial rEcommendation model (TASTE), which maps items and users in an embedding space and recommends items by matching their text representations. TASTE verbalizes items and user-item interactions using identifiers and attributes of items. To better characterize user behaviors, TASTE additionally proposes an attention sparsity method, which enables TASTE to model longer user-item interactions by reducing the self-attention computations during encoding. Our experiments show that TASTE outperforms the state-of-the-art methods on widely used sequential recommendation datasets. TASTE alleviates the cold start problem by representing long-tail items using full-text modeling and bringing the benefits of pretrained language models to recommendation systems. Our further analyses illustrate that TASTE significantly improves the recommendation accuracy by reducing the popularity bias of previous item id based recommendation models and returning more appropriate and text-relevant items to satisfy users. All codes are available at https://github.com/OpenMatch/TASTE.