Modern supercomputing clusters frequently incorporate Graphics Processing Units (GPUs) as accelerators for highly-parallel floating-point computations. However, due to the cost of GPUs it is often not feasible to provide a GPU for each node in the cluster, resulting in the need to share a single GPU as a virtual resource among several nodes. Traditional GPUs use batch-style FIFO scheduling, which does not fairness among jobs from different users or of different lengths. We propose a fairness-aware GPU scheduler to provide fairness among jobs on a shared virtual GPU resource.