The aim of this paper is to establish the existence of at least three solutions for the nonlinear Neumann boundary-value problem involving the p(x)-Laplacian of the form $-{\Delta }_{p\left(x\right)}u+a\left(x\right)|u^{\left|p\right(x)-2}u=\mu g(x,u)$ in Ω, ${\left|\nabla u\right|}^{p\left(x\right)-2}\partial u/\partial \nu =\lambda f(x,u)$ on ∂Ω. Our technical approach is based on the three critical points theorem due to Ricceri.