There is great interest in developing radiological classifiers for diagnosis, staging, and predictive modeling in progressive diseases such as Parkinson's disease (PD), a neurodegenerative disease that is difficult to detect in its early stages. Here we leverage severity-based meta-data on the stages of disease to define a curriculum for training a deep convolutional neural network (CNN). Typically, deep learning networks are trained by randomly selecting samples in each mini-batch. By contrast, curriculum learning is a training strategy that aims to boost classifier performance by starting with examples that are easier to classify. Here we define a curriculum to progressively increase the difficulty of the training data corresponding to the Hoehn and Yahr (H&Y) staging system for PD (total N=1,012; 653 PD patients, 359 controls; age range: 20.0-84.9 years). Even with our multi-task setting using pre-trained CNNs and transfer learning, PD classification based on T1-weighted (T1-w) MRI was challenging (ROC AUC: 0.59-0.65), but curriculum training boosted performance (by 3.9%) compared to our baseline model. Future work with multimodal imaging may further boost performance.