In this work, shape optimization of a wire-wrapped fuel assembly in a liquid metal reactor has been carried out by combining a three-dimensional Reynolds-averaged Navier-Stokes analysis with the radial basis neural network method, a well known surrogate modeling technique for optimization. Sequential Quadratic Programming is used to search the optimal point from the constructed surrogate. Two geometric design variables are selected for the optimization and design space is sampled using Latin Hypercube Sampling. The optimization problem has been defined as a maximization of the objective function, which is as a linear combination of heat transfer and friction loss related terms with a weighing factor. The objective function value is more sensitive to the ratio of the wire spacer diameter to the fuel rod diameter than to the ratio of the wire wrap pitch to the fuel rod diameter. The optimal values of the design variables are obtained by varying the weighting factor.