Graphics Processing Units (GPUs) have evolved over the years from being graphics accelerator to scalable coprocessor. We implement an algebraic multigrid solver for three dimensional unstructured grids using GPU. Such a solver has extensive applications in Computational Fluid Dynamics (CFD). Using a combination of vertex coloring, optimized memory representations, multi-grid and improved coarsening techniques, we obtain considerable speedup in our parallel implementation. Our solver provides significant acceleration for solving pressure Poisson equations, which is the most time consuming part while solving Navier-Stokes equations. In our experimental study, we solve pressure Poisson equations for flow over lid driven cavity and for laminar flow past square cylinder. Our implementation achieves 915 times speed up for the lid driven cavity problem on a grid of size 2.6 million and a speed up of 1020 times for the laminar flow past square cylinder problem on a grid of size 1.7 million, compared to serial non-multigrid implementations. For our implementation, we used NVIDIA's CUDA programming model. © 2014 IEEE.