This manuscript discusses the existence of nontrivial weak solution for the following nonlinear eigenvalue problem driven by the p(·)-biharmonic operator with Rellich-type term { ∆(|∆u|p(x)−2∆u) = λ |u| q(x)−2u/δ(x)2q(x) , for x ∈ Ω, u = ∆u = 0, for x ∈ ∂Ω. Considering the case 1 < min x∈Ω p(x) ≤ max x∈Ω p(x) < min x∈Ω q(x) ≤ max x∈Ω q(x) < min { N/ 2 , Np(x)/ N −2p(x) } , we extend the corresponding result of the reference [8], for the case 1 < min x∈Ω q(x) ≤ max x∈Ω q(x) < min x∈Ω p(x) ≤ max x∈Ω .p(x) < N 2 . The proofs of the main results are based on the mountain pass theorem.