In this paper, we study the following variational inequality u ∈ K, ⟨Au, v − u⟩ + ∫ Ω 1(x,u)(v − u) ≥ ∫ Ω f (x,u,∇u)(v − u),∀v ∈ K, where K = {u ∈ W1,p0 (Ω) : u(x) ≥ 0}, A is the p- Laplacian and the function 1 is increasing in the second variable. By constructing the solution operator for an associate variational inequality, we reduce the problem to a fixed point equation. Then, we apply the fixed point index to prove the existence of the nontrivial solution of the problem.