The Murchison Widefield Array (MWA) is a new 80-300 MHz synthesis radio telescope under construction in Western Australia. The science objectives of the MWA include the epoch of reionization, the heliosphere, the ionosphere, transients and a Southern sky survey. The 500 antennas of the telescope will generate 16GB/s of raw visibilities, which must be processed in real-time including calibration of the instrument and ionosphere. A dedicated supercomputer is required for this task. Modern, PC-based Graphics Processing Units (GPUs), originally developed for computer games, offer close to Tflop/s performance as a cheap, off-the-shelf component. With the development of easy to use programming tools, GPUs can be used by the scientific community for compute-intensive tasks. Much of the processing for the MWA real-time system is particularly well suited to GPUs. We describe the types of algorithms used in the real-time system and the improvement in runtime that has been achieved using an nVidia G80-based GPU compared to a regular CPU. We estimate that a GPU-based real-time supercomputer for the MWA would be able to process the data with an order of magnitude fewer nodes than a traditional cluster.