A passive split-and-recombine micromixer was developed based on the concept of lamellar structure and advection mixing type for a serpentine structure. The flow patterns and mixing performance were analyzed using numerical simulation in Reynolds number range of 10≤ Reynolds ≤170. Two design variables, defining the shape of the split-and-recombine branch, were optimized by the local energy dissipation rate as the objective function. The reduction of computation time and the absence of numerical diffusion were the advantages of using the energy dissipation rate as the objective function. At each Reynolds number, 64 sample data was generated on the design space uniformly. Then a model was used based on the Radial basis neural network for the prediction of the objective function. The optimum values of the design variables within the constraint range were found on the response surface. The optimization study was performed at five Reynolds numbers of 10, 50, 90, 130, 170 and the mixing index was improved 0.156, 0.298, 0.417, 0.506, and 0.57, respectively. The effect of design variables on the objective function and the concentration pattern was presented and analyzed. Finally, the mixing characteristic of the split-and-recombine micromixer was studied in a wide range of Reynolds number and the flow was categorized to stratify and show the vortex regime based on the Reynolds number. The optimized split-and-recombine micromixer could be integrated by any system depending on the desired velocity and Reynolds number.