Cataracts, which result from lens opacification, are the leading cause of blindness worldwide. Current methods for determining the severity of cataracts are based on manual assessments that may be weakened by subjectivity. In this work, we propose a system to automatically grade the severity of nuclear cataracts from slit-lamp images. We introduce a new feature for cataract grading together with a group sparsity-based constraint for linear regression, which performs feature selection, parameter selection and regression model training simultaneously. In experiments on a large database of 5378 images, our system outperforms the state-of-the-art by yielding with respect to clinical grading a mean absolute error (epsilon) of 0.336, a 69.0% exact integral agreement ratio (R0), a 85.2% decimal grading error < or = 0.5 (Re0.5), and a 98.9% decimal grading error < or = 1.0 (Re1.0). Through a more objective grading of cataracts using our proposed system, there is potential for better clinical management of the disease.