Lumbar disc degeneration (LDD) is a commonly age-associated condition related to low back pain, while its consequences are responsible for over 90% of spine surgical procedures. In clinical practice, grading of LDD by inspecting MRI is a necessary step to make a suitable treatment plan. This step purely relies on physicians manual inspection so that it brings the unbearable tediousness and inefficiency. An automated method for grading of LDD is highly desirable. However, the technical implementation faces a big challenge from class ambiguity, which is typical in medical image classification problems with a large number of classes. This typical challenge is derived from the complexity and diversity of medical images, which lead to a serious class overlapping and brings a great challenge in discriminating different classes. To solve this problem, we proposed an automated grading approach, which is based on supervised distance metric learning to classify the input discs into four class labels (0: normal, 1: slight, 2: marked, 3: severe). By learning distance metrics from labeled instances, an optimal distance metric is modeled and with two attractive advantages: (1) keeps images from the same classes close, and (2) keeps images from different classes far apart. The experiments, performed in 93 subjects, demonstrated the superiority of our method with accuracy 0.9226, sensitivity 0.9655, specificity 0.9083, F-score 0.8615. With our approach, physicians will be free from the tediousness and patients will be provided an effective treatment.