Software testing is one of the most crucial parts of the software development life cycle. Developers spend substantial amount of time and efforts on software testing. Recently, there has been a growing scholarly interest in the automation of software testing. However, recent studies have revealed significant limitations in the quality and efficacy of the generated assert statements. These limitations primarily arise due to: (i) the inherent complexity involved in generating assert statements that are both meaningful and effective; (ii) the challenge of capturing the relationship between multiple assertions in a single test case. In recent research, deep learning techniques have been employed to generate meaningful assertions. However, it is typical for a single assertion to be generated for each test case, which contradicts the current situation where over 40% of test cases contain multiple assertions. To address these open challenges, we propose a novel approach, called DeepAssert that exploits the pre-trained model GraphCodeBERT to automatically generate multiple assertions for test methods. It can recommend a sequence of assert statements effectively given a test method and a focal method (the method under test). To evaluate the effectiveness of our approach, we conduct extensive experiments on the dataset built on the top of Methods2Test dataset. Experimental results show that DeepAssert achieves scores of 54.16%, 18.36%, and 15.38% in terms of CodeBLEU, Accuracy and perfect prediction and substantially outperforms the state-of-the-art baselines by a large margin. Furthermore, we evaluate the effectiveness of DeepAssert on the task of bug detection and the result indicates that the assert sequences generated by DeepAssert can assist in exposing 51 real-world bugs extracting from Defects4J while only considering the first compiled assert sequence, outperforming the SOTA approaches by a large margin as well.