We study the following nonlinear problem $-div(w(x){mid}{ abla}u{mid}^{p(x)-2}{ abla}u)+{mid}u{mid}^{p(x)-2}u={lambda}f(x,u)$ in ${Omega}$ which is subject to Neumann boundary condition. Under suitable conditions on w and f, we give the existence of a positive infimum eigenvalue for the p(x)-Laplacian Neumann problem.