The QUICKER scheme extended for non-uniform rectangular grid systems has been applied to predict the turbulent offset jet flows. Computational results obtained with the QUICKER scheme are compared with those from the skew-upwind and the hybrid schemes. Computational results include the reattachment length, the velocity profile, the axial velocity decay curve, and the shear stress distribution. In the sense of an overall agreement with the experimental data, the QUICKER scheme is found to be superior to the other two schemes. Boundary conditions are carefully set up to account for various flow conditions. Special attention has been given to the set-up of entrainment boundary condition. It is emphasized that the numerical diffusion due to streamline-to-grid skewness far exceeds the turbulent diffusion in offset jet flows; therefore, a numerical scheme that would minimize the numerical diffusion is a prerequisite for a better prediction of the turbulent offset jet flows.