This paper presents GPU parallelization for a computational fluid dynamics solver which works on a mesh consisting of polyhedral cells, where each cell has an arbitrary number of faces and each face has an arbitrary number of vertices. The parallelization is achieved using NVIDIAs compute unified device architecture (CUDA). The developed code specifically targets performance improvement on NVIDIA Tesla accelerator GPUs. The implementation has been carried out in a general purpose open-source CFD framework namely OpenFOAM which is capable of solving arbitrary flow problems involving complex geometries with polyhedral unstructured grids. The present work considers incompressible flow simulations, where solving pressure Poisson equation is the most computationally expensive step. The Poisson equation is solved using conjugate gradient method preconditioned by algebraic multigrid method. This part of the solver is outsourced by OpenFOAM to GPU. The GPU pressure Poisson solver acceleration is determined with respect to OpenFOAM serial version (single cpu core) and MPI parallelized version (8 cpu cores). The GPU solver acceleration was tested by simulating a standard benchmark test case called lid driven cavity flow for different grid sizes. The current GPU based solver has shown a speedup of approximately 16× when compared to single cpu core and 3.3 × when compared to OpenFOAM MPI version using 8 cpu cores, for a grid size of 5 million cells. © 2016 IEEE.