The Gaussian wave functional method is applied to a boson system with an array of local potentials cos［β（ｎR）］to study the phase transition of its ground of its ground state. The stable ground state is determined by the parameter γ＝β2/4π and the renormalized mass μ．In different regions, μ can have different multiplicity, the phase diagram is thus depicted. The phase boundary γ＝γ1 depends on the concentration c; for c←0, it coincides with that of the single impurity model, while for γ=2 it coincides with the conclusion of the continuous model.