Optimization of a three-dimensional split-and-recombine micromixer with serpentine structure was performed using Navier-Stokes analysis and optimization techniques. The optimization study was performed at a fixed Reynolds number of 15, with four dimensionless design variables, viz. the ratio of the subchannel width to the main channel width, the ratio of the subchannel length to the pitch length, the ratio of the subchannel depth to the main channel depth, and the ratio of the recombination channel width to the main channel width. The design space was investigated by a parametric study, and the design points within the design space were selected by the Latin hypercube sampling method. Two different objective functions, viz. the mixing index at the micromixer exit and mixing effectiveness, were used alternately for the single-objective optimizations. Mixing effectiveness was defined as the ratio of the mixing index to the pressure drop. A surrogate modeling technique based on a radial basis neural network was used to approximate the objective functions. Optimum configurations of the micromixer were found through the mixing-index and mixing-effectiveness optimizations. The optimum design of the micromixer obtained by the mixing-index optimization confirmed 33.0% relative increase in the mixing index compared with the reference micromixer. The mixing index, 0.86, which was achieved by the optimization of the micromixer, is much higher than those of the other split-and-recombine micromixers at the same mixing length and Reynolds number, and the optimized micromixer could be integrated with microfluidic systems including lab on a chip and micro total analysis system.