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 . More precisely, we consider where is an open bounded domain with Lipschitz boundary with m > 1, a > 0, b > 0, dimension is the fractional critical Sobolev exponent, and the parameters λ > 0, 0 < s < 1 < q < p < ∞. Applying the Nehari manifold, fibering maps and Krasnoselskii genus theory, we investigate the existence and multiplicity of nonnegative solutions.