In this work multiobjective shape optimization of a 19-pin wire-wrapped fuel assembly is carried out using a hybrid multiobjective evolutionary approach in order to achieve an acceptable compromise between two competing objectives, i.e., enhancement of heat transfer and reduction of friction loss. Two nondimensional variables, wire-spacer diameter to fuel rod diameter ratio and wire-wrap pitch to fuel rod diameter ratio, are chosen as design variables. The response surface approximation method is used to construct the surrogate with objective function values calculated by means of Reynolds-averaged Navier-Stokes analysis of the flow and heat transfer. The shear stress transport turbulence model is used as a turbulence closure. The optimization results are processed by the Pareto-optimal method. The Pareto-optimal solutions are obtained using a combination of the evolutionary algorithm NSGA-II and a local search method. The Pareto-optimal front for the wire-wrapped fuel assembly has been obtained. With an increase in the wire-spacer diameter, both heat transfer and friction loss in the assembly increase. The design with higher heat transfer on the Pareto-optimal curve shows not only a lower maximum temperature but also a more uniform temperature distribution on the cross section of the assembly in comparison with the other designs.