In the present work, shape of the mixing vane in Plus7 fuel assembly has been optimized numerically using three-dimensional Reynolds-averaged Navier-Stokes analysis of flow and heat transfer. Standard $k-{epsilon}$ model is used as a turbulence closure. The Response surface method is employed as an optimization technique. The objective function is defined as a combination of heat transfer rate and inverse of friction loss. Bend angle and base length of mixing vane are selected as design variables. Thermal-hydraulic performances for different shapes of mixing vane have been discussed, and optimum shape has been obtained as a function of weighting factor in the objective function.