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In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧$-(a+b{\int }_{\Omega }\left|\nabla u\right|²dx)\Delta u=u⁵+\lambda u^{q-1}/{\left|x\right|}^{\beta }$ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.