The MWA is a next-generation radio interferometer under construction in remote Western Australia. The data rate from the correlator makes storing the raw data infeasible, so the data must be processed in real-time. The processing task is of order ~10 TFLOPS. The remote location of the MWA limits the power that can be allocated to computing. We describe the design and implementation of elements of the MWA real-time data processing system which leverage the computing abilities of modern graphics processing units (GPUs). The matrix algebra and texture mapping capabilities of GPUs are well suited to the majority of tasks involved in real-time calibration and imaging. Considerable performance advantages over a conventional CPU-based reference implementation are obtained.