Abstract: Recently,with the increase of the invasive species, multi-group reaction diffusion model has been used in invasion ecology theory. The multi-group reaction diffusion model can combine the spatial and population process within the prediction of invasion rate, also the use of continuous parameters in the model made it free to broad spatial scale. To simulate the phenomenon of two kinds of invasive species invading the native specie, Kim and Lin\citekl introduced a nonlinear weakly-coupled reaction diffusion system in the three-species model. The initial boundary value problem of the aforementioned model is concerned.By using the method of upper and lower solutions as well as iteration, sufficient condition is obtained for the global asymptotic stability of the trivial solution and the nonnegative semitrivial solutions with the homogeneous Neumann boundary condition. The results reveal by means of controlling the birth rate, interspecific, intraspecific interaction rate of populations to achieve the goal of certain population disappearance or certain population persistence. These conditions are easy to check, and the independent of the diffusion rates and thus the conclusions are also appropriate for the corresponding parabolic-ordinary differential system( d_i=0 for some or all i).