Shape optimization of an upper plenum of a PBMR type gas cooled nuclear reactor has been performed by using three-dimensional Reynolds-Averaged Navier-Stokes (RANS) analysis and surrogate modeling technique. The objective function is defined as a linear combination of uniformity of flow distribution in the core and pressure drop in the upper plenum and the core. The ratio of thickness of slot to diameter of rising channels, ratio of height of upper plenum to diameter of rising channels, and ratio of height of the slot at inlet to outlet, are used as design variables for optimization. Design points are selected through Latin-hypercube sampling. The optimal point is determined through surrogate-based optimization method which uses 3-D RANS analyses at design points. The results show that the optimum shape represent remarkably improved performance in flow uniformity and friction loss than the reference shape.