An active micro-mixer, which is composed of an oscillating micro-stirrer in the micro-channel to provide effective mixing was optimized. The effects of molecular diffusion and disturbance by the stirrer were considered with regard to two types of mixer models: the simple straight micro-channel and micro-channel 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 were compared. From the results, it was found that the mixer with an oscillating stirrer was much more enhanced and stabilized. Therefore, an approximate optimization of an active micro-mixer with an oscillating stirrer was performed using Kriging method with OLHD(Optimal Latin Hypercube Design) in order to determine the optimal design variables. The design parameters were established as the frequency, the length and the angle of the stirrer. The optimal values were obtained as 1.0346, 0.66D and $pm45^{circ}$, respectively. It was found that the mixing index of the optimal design increased by 88.72% compared with that of the original design.