A two-component lattice Boltzmann method(LBM)with a multiple-relaxation-time(MRT)collision operator is pre-sented to improve the numerical stability of the single relaxation time(SRT)model.The macroscopic and the momentum conservation equations can be retrieved through the Chapman-Enskog(C-E)expansion analysis.The equilibrium mo-ment with the diffusion term is calculated,a diffusion phenomenon is simulated by utilizing the developed model,and the numerical stability is verified.Furthermore,the binary mixture channel model is designed to simulate the sound attenua-tion phenomenon,and the obtained simulation results are found to be consistent with the analytical solutions.The sound attenuation model is used to study the numerical stability and calculation accuracy of the LBM model.The simulation results show the stability and accuracy of the MRT model and the SRT model under different viscosity conditions.Finally,we study the influence of the error between the macroscopic equation of the MRT model and the standard incompressible Navier-Stokes equation on the calculation accuracy of the model to demonstrate the general applicability of the conclusions drawn by the sound attenuation model in the present study.