Lung cancer has the highest mortality rate of deadly cancers in the world. Early detection is essential to treatment of lung cancer. However, detection and accurate diagnosis of pulmonary nodules depend heavily on the experiences of radiologists and can be a heavy workload for them. Computer-aided diagnosis (CAD) systems have been developed to assist radiologists in nodule detection and diagnosis, greatly easing the workload while increasing diagnosis accuracy. Recent development of deep learning, greatly improved the performance of CAD systems. However, lack of model reliability and interpretability remains a major obstacle for its large-scale clinical application. In this work, we proposed a multi-task explainable deep-learning model for pulmonary nodule diagnosis. Our neural model can not only predict lesion malignancy but also identify relevant manifestations. Further, the location of each manifestation can also be visualized for visual interpretability. Our proposed neural model achieved a test AUC of 0.992 on LIDC public dataset and a test AUC of 0.923 on our in-house dataset. Moreover, our experimental results proved that by incorporating manifestation identification tasks into the multi-task model, the accuracy of the malignancy classification can also be improved. This multi-task explainable model may provide a scheme for better interaction with the radiologists in a clinical environment.