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We establish the existence of positive bound state solutions for the singular quasilinear Schrodinger equation iψ/t=-div(ρ(|ψ|^2) ψ)+ω(|ψ|62)ψ-λρ(|ψ|^2)ψ,x∈Ω,t〉0,where ω(τ^2)τ→∞ as τ→ 0 and, λ 〉 0is a parameter and Ω is a ball in ^RN. This problem is studied in connection with the following quasilinear eigenvalue problem with Dirichlet boundary condition -div(ρ(| ψ|^2) ψ)=λ1ρ(|ψ|^2)ψ=λ1ρ(|ψ|^2)ψ,x∈Ω.Indeed, we establish the existence of solutions for the above Schrodinger equation when A belongs to a certain neighborhood of the first eigenvahie λ1 of this eigenvalue problem. The main feature of this paper is that the nonlinearity ω|ψ|^2 is unbounded around the origin and also the presence of the second order nonlinear term. Our analysis shows the importance of the role played by the parameter A combined with the nonlinear nonhomogeneous term div (ρ(| ψ|^2) ψ) which leads us to treat this prob- lem in an appropriate Orlicz space. The proofs are based on various techniques related to variational methods and implicit function theorem.