Based on the Bhatangar-Gross-Krook (BGK) models, numerical simulation using the lattice Boltzmann model is performed to investigate the optimized surface patte in a micro-channel. In order to simulate the practical situation correctly, a slip/no-slip boundary condition is applied with making several assumptions. To assess the validity and efficiency of the model, one benchmark problem with considering the surface pattes is studied.Numerical results show the value of rms velocity Vrms increases with the increasing ratioβ and larger Reynolds number Re, higher fluctuation of the rms oscillating velocity. Furthermore, the results show that a good mixing effect can be obtained when Re is large enough and the ratioβ is about 1.618, which is the appropriate choice,i.e. the well known golden section phenomenon.