The radial basis neural network (RBNN) method has been applied to shape optimization of a staggered herringbone groove micromixer using three-dimensional Navier-Stokes analysis. The calculation of the variance of the mass fraction at various nodes on a plane in the channel is used to quantify the mixing. Optimization techniques based on the RBNN method are used to optimize the shape of the grooves on a single wall of the channel. Three design variables, i.e., the ratio of the groove depth to channel height, the ratio of the groove width to groove pitch, and the angle of the groove, are selected for optimization. The mixing index at the end of the patterned groove is employed as the objective function. The dependence of the objective function on the design variables is analyzed. The RBNN method is successfully applied to improve the degree of mixing with modification of the groove shape.