We introduce a GPU-accelerated finite element forward solver for the computation of light transport in scattering media. The forward model is the computationally most expensive component of iterative methods for image reconstruction in diffuse optical tomography, and performance optimisation of the forward solver is therefore crucial for improving the efficiency of the solution of the inverse problem. The GPU forward solver uses a CUDA implementation that evaluates on the graphics hardware the sparse linear system arising in the finite element formulation of the diffusion equation. We present solutions for both time-domain and frequency-domain problems. A comparison with a CPU-based implementation shows significant performance gains of the graphics accelerated solution, with improvements of approximately a factor of 10 for double-precision computations, and factors beyond 20 for single-precision computations. The gains are also shown to be dependent on the mesh complexity, where the largest gains are achieved for high mesh resolutions.