Idiopathic Parkinsons disease and atypical parkinsonian syndromes have similar symptoms at early disease stages, which makes the early differential diagnosis difficult. Positron emission tomography with 18F-FDG shows the ability to assess early neuronal dysfunction of neurodegenerative diseases and is well established for clinical use. In the past decades, machine learning methods have been widely used for the differential diagnosis of parkinsonism based on metabolic patterns. Unlike these conventional machine learning methods relying on hand-crafted features, the deep convolutional neural networks, which have achieved significant success in medical applications recently, have the advantage of learning salient feature representations automatically and effectively. This advantage may offer more appropriate invisible features extracted from data for the enhancement of the diagnosis accuracy. Therefore, this paper develops a 3D deep convolutional neural network on 18F-FDG PET images for the automated early diagnosis. Furthermore, we depicted in saliency maps the decision mechanism of the deep learning method to assist the physiological interpretation of deep learning performance. The proposed method was evaluated on a dataset with 920 patients. In addition to improving the accuracy in the differential diagnosis of parkinsonism compared to state-of-the-art approaches, the deep learning methods also discovered saliency features in a number of critical regions (e.g., midbrain), which are widely accepted as characteristic pathological regions for movement disorders but were ignored in the conventional analysis of FDG PET images.