Elbow fractures are one of the most common fracture types. Diagnoses on elbow fractures often need the help of radiographic imaging to be read and analyzed by a specialized radiologist with years of training. Thanks to the recent advances of deep learning, a model that can classify and detect different types of bone fractures needs only hours of training and has shown promising results. However, most existing deep learning models are purely data-driven, lacking incorporation of known domain knowledge from human experts. In this work, we propose a novel deep learning method to diagnose elbow fracture from elbow X-ray images by integrating domain-specific medical knowledge into a curriculum learning framework. In our method, the training data are permutated by sampling without replacement at the beginning of each training epoch. The sampling probability of each training sample is guided by a scoring criterion constructed based on clinically known knowledge from human experts, where the scoring indicates the diagnosis difficultness of different elbow fracture subtypes. We also propose an algorithm that updates the sampling probabilities at each epoch, which is applicable to other sampling-based curriculum learning frameworks. We design an experiment with 1865 elbow X-ray images for a fracture/normal binary classification task and compare our proposed method to a baseline method and a previous method using multiple metrics. Our results show that the proposed method achieves the highest classification performance. Also, our proposed probability update algorithm boosts the performance of the previous method.