The widespread adoption of on-board volumetric imaging in cancer radiotherapy has stimulated research efforts to develop online adaptive radiotherapy techniques to handle the inter-fraction variation of the patient's geometry. Such efforts face major technical challenges to perform treatment planning in real time. To overcome this challenge, we are developing a supercomputing online re-planning environment (SCORE) at the University of California, San Diego (UCSD). As part of the SCORE project, this paper presents our work on the implementation of an intensity-modulated radiation therapy (IMRT) optimization algorithm on graphics processing units (GPUs). We adopt a penalty-based quadratic optimization model, which is solved by using a gradient projection method with Armijo's line search rule. Our optimization algorithm has been implemented in CUDA for parallel GPU computing as well as in C for serial CPU computing for comparison purpose. A prostate IMRT case with various beamlet and voxel sizes was used to evaluate our implementation. On an NVIDIA Tesla C1060 GPU card, we have achieved speedup factors of 20-40 without losing accuracy, compared to the results from an Intel Xeon 2.27 GHz CPU. For a specific nine-field prostate IMRT case with 5 x 5 mm(2) beamlet size and 2.5 x 2.5 x 2.5 mm(3) voxel size, our GPU implementation takes only 2.8 s to generate an optimal IMRT plan. Our work has therefore solved a major problem in developing online re-planning technologies for adaptive radiotherapy.