This paper is devoted to the following p -Kirchhoff type of problems − a + b ∫ Ω ∇ u p d x Δ p u = f x , u , x ∈ Ω u = 0 , x ∈ ∂ Ω with the Dirichlet boundary value. We show that the p -Kirchhoff type of problems has at least a nontrivial weak solution. The main tools are variational method, critical point theory, and mountain-pass theorem.