Legal Judgment Prediction (LJP) aims to predict the judgment result based on the fact description of a criminal case, and is gradually becoming a hot research topic in the legal realm. Generally, a classic LJP contains three subtasks, i.e., applicable law article prediction, charge prediction, and term of penalty prediction. In real-world scenarios, both charge prediction and applicable law article prediction are actually the tasks of multi-class classification with multi-label learning. However, most existing studies model them as the problems of multi-class classification with single-label learning. Besides, they only consider the context of the fact description, and ignore the exploitation of effective keywords that are widely existed in abundant law articles. To fill the above gaps, we propose a novel multi-task legal judgment prediction framework via multi-view encoder fusing legal keywords, named MVE-FLK, to jointly model multiple subtasks in LJP. Specifically, the multi-view encoder is the core module of MVE-FLK, in this module, we devise a word and sentence encoder (WSE) with an attention mechanism to fuse legal keywords. And then, we develop a multi-view attention network to combine WSE with classic Transformer and DAN (Deep Averaging Network) for encoding the case from multiple views. After that, we propose a multi-task prediction module by developing a novel keywords fusing approach to enhance the performance of multi-task prediction. In addition, we devise a unique prediction principle for each subtask at a fine-grained level, which effectively improves the performance of subtasks. The experimental results on two real-life legal datasets show that our model yields significant prediction performance advantages over six competitive methods.