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This paper is concerned with the existences of positive solutions of the following Dirichlet problem for p-mean curvature operator with supercritical potential: -div((1 + |∇u|²) ^p-22 ∇u) = λu^r-1 + μu^q-1 |x|^s, u > 0 ∈ Ω, u = 0x ∈ ∂Ω where u Ω W^1, p_0 (Ω), Ω is a bounded domain in R^N(N > p > 1) with smooth boundary ∂Ω and 0 ∈ Ω, 0 < q < p, 0 ≤ s < Np (p - q) + q, p ≤ r < p∗, p∗ = NpN-p, μ > 0. It reaches the conclusion where this problem has two positive solutions in the different cases . It discusses the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with supercritical potential firstly. Meanwhile, it extends some results of the p-Laplace operator to that of p-mean curvature operator for p ≥ 2 . , number=3, journal=Journal of Partial Differential Equations, year=2005, month=Aug., pages=193–205