Both computational and experimental results are presented for studying the three-dimensional flow in an annular gas turbine combustor. The computational approach attempts to strike a reasonable balance to handle the competing aspects of the complicated physical and chemical interactions of the flow, and the requirements in resolving the three-dimensional geometrical constraints of the combustor contours, film cooling slots, and circular dilution holes. The algorithm employs non-orthogonal curvilinear coordinates, second-order accurate discretizations, multigrid iterative solution procedure, the standard k-ε turbulence model, and a combustion model comprising of an assumed probability density function and the conserved scalar variable formulation. To assess the performance of the numerical algorithm, three different annular combustor flows with in-house experimental measurements are investigated. Overall, it is found that good theory/data agreement of the characteristic temperature pattern in the exit plane can be obtained. The influence of changing the dilution hole arrangements on the combustor performance is well predicted. The complicated mixing process can be better understood with more detailed information supplied by the numerical simulation. It is concluded that for the normal operating condition where the physical process is likely to be dominant, the performance of a gas turbine combustor can be predicted by the present methodology.