In this paper, we prove, in the spirit of [3, 12, 20, 22, 23], the existence of infinitely many small solutions to the following quasilinear elliptic equation $-{Delta}_{p(x)}u+{mid}u{mid}^{p(x)-2}u={mid}u{mid}^{q(x)-2}u+{lambda}f(x,u)$ in a smooth bounded domain ${Omega}$ of ${mathbb{R}}^N$. We also assume that ${q(x)=p^*(x)}{ eq}{emptyset}$, where $p^*(x)$ = Np(x)/(N - p(x)) is the critical Sobolev exponent for variable exponents. The proof is based on a new version of the symmetric mountainpass lemma due to Kajikiya [22], and property of these solutions are also obtained.