An active micro-mixer, which was composed of an oscillating micro-stirrer in the microchannel to provide rapid, effective mixing at high flow, rates was analyzed. The effects of molecular diffusion and disturbance by the stirrer were considered with regard to two types of mixer models: the simple straight microchannel and microchannel with an oscillating stirrer. Two types of mixer models were studied by analyzing mixing behaviors such as their interaction after the stirrer. The mixing was calculated by Lattice Boltzmann methods using the D2Q9 model. In this study, the time-averaged mixing index formula was used to estimate the mixing performance of time-dependent flow. The mixing indices of the two models compared. From the results, it was found that the mixer with an oscillating stirrer was much more enhanced and stabilized. Therefore, an optimum design for a dynamic micro-mixer with an oscillating stirrer was performed using Taguchi method in order to obtain a robust solution. The design parameters were established as the frequency, the length and the angle of the stirrer and the optimal values were determined to be 2, 0.8D and ${pm}75^{circ}$, respectively. It was found that the mixing index of the optimal design increased 80.72% compared with that of the original design.