Surrogate models have been applied to shape optimizations of a micromixer with the aim of assessing the performance of the models. The surrogate models considered include polynomial response surface approximation, Kriging, and radial basis neural network. In addition, a weighted average model based on global error measures is constructed. A mixing index at the exit of the micromixer is used as the objective function. The mixing index is calculated based on Navier-Stokes equations. Two cases of optimization, one with two design variables and the other with three design variables, have been tested. The design variables are selected among the ratio of the groove depth to channel height, the angle of groove, and the ratio of groove width to groove pitch. D-Optimal design generated sampling points are used for sampling. It is found that although the weighted average model does not predict the best optimal point, it does show consistent and reliable performance.