To build an interpretable neural text classifier, most of the prior work has focused on designing inherently interpretable models or finding faithful explanations. A new line of work on improving model interpretability has just started, and many existing methods require either prior information or human annotations as additional inputs in training. To address this limitation, we propose the variational word mask (VMASK) method to automatically learn task-specific important words and reduce irrelevant information on classification, which ultimately improves the interpretability of model predictions. The proposed method is evaluated with three neural text classifiers (CNN, LSTM, and BERT) on seven benchmark text classification datasets. Experiments show the effectiveness of VMASK in improving both model prediction accuracy and interpretability.