Effective mixing plays a crucial role in microfluidics for biochemical applications. Owing to the small device scale and its entailing the low Reynolds number, the mixing in microchannels proceeds very slowly. In this work, we optimize the configuration of obstacles in the Y-channel mixer in order to attain maximum mixing efficiency. Before the optimum design, mixing characteristics are investigated using unstructured grid CFD method. Then, the analysis method is employed to construct the approximate analysis model to be used in the optimization procedure. The main optimization tool in the present work is sequential quadratic programming method. Using this approximate optimization procedure, we may obtain the optimum layout of obstacles in the Y-channel mixer in an efficient manner, which gives the maximum mixing efficiency.