The aim of this paper is to study the existence and multiplicity of nonnegative solutions for the following critical Kirchhoff equation involving the fractional p-Laplace operator ( − Δ)ps. More precisely, we consider $$ M\left(^{2N}}}{|x-y|^{N+ps}}dxdy\right)(-\Delta)_{p}^{s} u=\lambda f(x)|u|^{q-2}u+K(x)|u|^{p_{s}^{*}-2}u,\quad &{\rm in}\ \Omega,\\ u=0, \quad\quad &{\rm in}\ ^{N}\setminus \Omega, \\ $$ where Ω ⊂ ℝN is an open bounded domain with Lipschitz boundary ∂Ω, M(t)=a + btm − 1 with m > 1, a > 0, b > 0, dimension N > sp, $ p_{s}^{*}={N-ps}$ is the fractional critical Sobolev exponent, and the parameters λ > 0, 0 < s < 1 < q < p < ∞. Applying Nehari manifold, fibering maps and Krasnoselskii genus theory, we investigate the existence and multiplicity of nonnegative solutions.