Computerized Adaptive Testing(CAT) refers to an online system that adaptively selects the best-suited question for students with various abilities based on their historical response records. Most CAT methods only focus on the quality objective of predicting the student ability accurately, but neglect concept diversity or question exposure control, which are important considerations in ensuring the performance and validity of CAT. Besides, the students' response records contain valuable relational information between questions and knowledge concepts. The previous methods ignore this relational information, resulting in the selection of sub-optimal test questions. To address these challenges, we propose a Graph-Enhanced Multi-Objective method for CAT (GMOCAT). Firstly, three objectives, namely quality, diversity and novelty, are introduced into the Scalarized Multi-Objective Reinforcement Learning framework of CAT, which respectively correspond to improving the prediction accuracy, increasing the concept diversity and reducing the question exposure. We use an Actor-Critic Recommender to select questions and optimize three objectives simultaneously by the scalarization function. Secondly, we utilize the graph neural network to learn relation-aware embeddings of questions and concepts. These embeddings are able to aggregate neighborhood information in the relation graphs between questions and concepts. We conduct experiments on three real-world educational datasets, and show that GMOCAT not only outperforms the state-of-the-art methods in the ability prediction, but also achieve superior performance in improving the concept diversity and alleviating the question exposure. Our code is available at https://github.com/justarter/GMOCAT.