We study the existence of nontrivial solutions of the p-Kirchhoff type equation with critical nonlinearity, where a > 0, b > 0, 1 < p < N, 1 < q < p, p ∗ = Np N - p, µ > 0, ∆ p u = div( |∇ u | p - 2 ∇ u) is the p-Laplacian of u, f ∈ L p ∗ p ∗- q ( R N ) \{ 0 } and f is nonnegative. Under certain conditions, we prove the existence of at least two nontrivial solutions of the above equation by the methods of Ekeland variation...