This paper proposes a multi-task learning algorithm to classify the Chinese legal questions using deep convolutional neural networks (CNN). First, we propose a multi-task Convolutional Neural Network (CNN) for classification of Chinese legal questions with trainable word embedding where coarse grained classification is the main task and fine grained classification is the side task. Second, we develop a hierarchical classification model which takes the output of coarse classification as one part of the input for fine grained classification. We find that the side task can improve the accuracy and efficiency of the classification in a certain extent. Our experiments on the entire Chinese Legal Questions Dataset (LQDS) demonstrate the effectiveness of the proposed approach. To the best of our knowledge, this is the first work using almost all data in LQDS for classification and we achieve the state of the art performance.