Applying invariant region method and with the aid of quadratic form theory we obtain a set of sufficient conditions for the globally asymptotic stability of the solutions to Cauchy problem for the n-species Lotka-Volterra tree systems of interacting population-diffusion equations. The criteria in this paper are in explicit forms of the parameters, and thus, are easily verifiable. Moreover, this criteria is applicable to competition model, cooperation model, as well as to predator-prey model.