GPUs in High-Performance Computing systems remain under-utilised due to the unavailability of schedulers that can safely schedule multiple applications to share the same GPU. The research reported in this paper is motivated to improve the utilisation of GPUs by proposing a framework, we refer to as schedGPU, to facilitate intra-node GPU co-scheduling such that a GPU can be safely shared among multiple applications by taking memory constraints into account. Two approaches, namely a client-server and a shared memory approach are explored. However, the shared memory approach is more suitable due to lower overheads when compared to the former approach. Four policies are proposed in schedGPU to handle applications that are waiting to access the GPU, two of which account for priorities. The feasibility of schedGPU is validated on three real-world applications. The key observation is that a performance gain is achieved. For single applications, a gain of over 10 times, as measured by GPU utilisation and GPU memory utilisation, is obtained. For workloads comprising multiple applications, a speed-up of up to 5x in the total execution time is noted. Moreover, the average GPU utilisation and average GPU memory utilisation is increased by 5 and 12 times, respectively.