Legal Judgment Prediction (LJP) aims to predict the judgment result based on the facts of a case and becomes a promising application of artificial intelligence techniques in the legal field. In real-world scenarios, legal judgment usually consists of multiple subtasks, such as the decisions of applicable law articles, charges, fines, and the term of penalty. Moreover, there exist topological dependencies among these subtasks. While most existing works only focus on a specific subtask of judgment prediction and ignore the dependencies among subtasks, we formalize the dependencies among subtasks as a Directed Acyclic Graph (DAG) and propose a topological multi-task learning framework, TopJudge, which incorporates multiple subtasks and DAG dependencies into judgment prediction. We conduct experiments on several real-world large-scale datasets of criminal cases in the civil law system. Experimental results show that our model achieves consistent and significant improvements over baselines on all judgment prediction tasks. The source code can be obtained from https://github.com/thunlp/TopJudge.