This paper presents numerical optimization of a rotating rectangular channel design with the staggered arrays of pinfins using Kriging meta-modeling technique. In the reference case, the channel aspect ratio (AR) is 4:1, the pin length to diameter ratio (H/D) is 2.0, and the pin spacing to diameter ratio is 2.0 in both the streamwise and spanwise directions. The rotation number is 0.15, while the Reynolds number based on hydraulic diameter is fixed at 10,000. Rotation of the channel slightly reduces the heat transfer on the leading surface and increases it on the trailing surface due to Coriolis effects. Two non-dimensional variables, the ratio of the height to diameter of the pinfin and the ratio of the spacing between the pinfins to diameter of the pinfins, are chosen as design variables. The objective function defined as a linear combination of heat transfer and friction loss related terms with a weighting factor is selected for the optimization. Twenty training points generated by Latin hypercube sampling (LHS) are evaluated by three-dimensional Reynolds-averaged Navier-Stokes (RANS) analysis with the shear stress transport (SST) model for the turbulence closure. The predictions of objective function by Kriging meta-modeling at optimum point show reasonable accuracy in comparison with the values calculated by RANS analysis. The results of optimization show that the cooling performance of the optimized shape is enhanced significantly through the optimization.