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This paper deals with the very weak solutions of A-harmonic equation divA(x, ∇u(x)) = 0 (∗) where the operator A satisfies the monotonicity inequality, the controllable growth condition and the homogeneity condition. The extremum principle for very weak solutions of A-harmonic equation is derived by using the stability result of Iwaniec-Hodge decomposition: There exists an integrable exponent r_1 = r_1(p, n, βα) = 12 [p - α100n²β + (p + α100n²β)² - 4α100n²β ] such that if u(x) ∈ W^1, r(Ω) is a very weak solution of the A-harmonic equation (∗), and m ≤ u(x) ≤ M on ∂Ω in the Sobolev sense, then m ≤ u(x) ≤ M almost everywhere in Ω, provided that r > r1. As a corollary, we prove that the 0-Dirichlet boundary value problem divA(x, ∇u(x)) = 0 u ∈ W^1, r_0 (Ω) of the A-harmonic equation has only zero solution if r > r_1. , number=3, journal=Journal of Partial Differential Equations, year=2005, month=Aug., pages=235–240