Parkinson's disease (PD) diagnosis is based on clinical criteria, i.e., bradykinesia, rest tremor, rigidity, etc. Assessment of the severity of PD symptoms with clinical rating scales, however, is subject to inter-rater variability. In this paper, we propose a deep learning based automatic PD diagnosis method using videos to assist the diagnosis in clinical practices. We deploy a 3D Convolutional Neural Network (CNN) as the baseline approach for the PD severity classification and show the effectiveness. Due to the lack of data in clinical field, we explore the possibility of transfer learning from non-medical dataset and show that PD severity classification can benefit from it. To bridge the domain discrepancy between medical and non-medical datasets, we let the network focus more on the subtle temporal visual cues, i.e., the frequency of tremors, by designing a Temporal Self-Attention (TSA) mechanism. Seven tasks from the Movement Disorders Society - Unified PD rating scale (MDS-UPDRS) part III are investigated, which reveal the symptoms of bradykinesia and postural tremors. Furthermore, we propose a multi-domain learning method to predict the patient-level PD severity through task-assembling. We show the effectiveness of TSA and task-assembling method on our PD video dataset empirically. We achieve the best MCC of 0.55 on binary task-level and 0.39 on three-class patient-level classification.