Achieving minimum pressure loss and exit temperature pattern factors are the two important, but conflicting performance goals of a gas turbine combustor. In this study, Taguchi method was used to design CFD (Computational Fluid Dynamics) analysis based experiments in order to arrive at optimized liner hole sizes (primary and dilution) of an annular gas turbine combustor. The CFD experiments were steady & three-dimensional Reynolds Averaged Navier-Stokes (RANS) based analyses performed on a 20-degree sector combustor model. Nine CFD analyses were performed as per the Taguchi L-9 orthogonal array, based on which, an optimal hole configuration was arrived. An additional CFD run was carried out to verify the predicted result. The optimized hole size combination reduces the Circumferential Pattern Factor (CPF) by 28% and pressure loss by 0.06% (difference between absolute values of percentage pressure losses) in comparison to the baseline configuration.