Legal Judgment Prediction (LJP) is a multi-task multi-label problem in the civil law system, involving the prediction of law articles, charges, and terms of penalty based on fact descriptions. However, most existing research approaches LJP as a single-label scenario, neglecting the correlations between multiple labels and failing to consider cross-task consistency constraints in a multi-label scenario. Moreover, although previous multi-task studies have proposed expert models and coarse-grained topology construction for inter-task relationships, the former neglects rich information exchange among different tasks, and the latter, if one task’s prediction is inaccurate, will affect subsequent tasks. This paper has designed legal label graphs and proposed a novel graph boosting with constraints framework, GJudge, for legal judgment prediction to address these limitations. The framework comprises a multi-perspective interactive encoder and a multi-graph attention consistency expert module. The encoder utilizes bidirectional LSTM, gated attention units, cross attention, and graph attention networks to integrate fact descriptions and label similarity relationships information from legal label graphs for multi-perspective interactive encoding. The expert module utilizes the multiple expert networks and the multi-graph attention network to differentiate between confusing labels and ensure consistent constraints across tasks, this is achieved through the fusion of label consistency constraints and confusion relationships information in the legal label graphs. Experimental results on two real-world datasets across different tasks show an improvement in F1 scores ranging from at least 0.93% to a maximum of 2.97%, illustrating the effectiveness of GJudge compared to the state-of-the-art model.