This paper reports the results of a numerical study on film cooling of an annular combustor liner with a combined slot and effusion geometry using three-dimensional steady state RANS approach. The combined film cooling geometry is realised by merging a slot fed by three-dimensional coolant jets (3D slot) with an effusion array. After performing grid convergence and validation study for the numerical model, the film cooling performance of both the two-dimensional planar slot and three-dimensional slot in the combined film method is compared at the same coolant mass flow rate to differentiate their cooling behavior. It is observed that at any given flow condition, the planar slot is over predicting effectiveness by more than 20% as compared to the 3D slot in the range of X/S = 0 to 20, where X/S is the non-dimensional streamwise distance from slot exit. The staggered pattern of effusion jets is seen to provide higher cooling than inline pattern. In view of this, further numerical studies are carried out with the three-dimensional slot coupled with the staggered effusion array. It is observed that the film effectiveness has a non-linear trend over a range of Mass Flow Ratios (MFRs) where the maximum laterally averaged adiabatic effectiveness is obtained at MFR = 5 for a blowing ratio of 1.2.