In this paper, we prove the existence of at least three weak solutions for a quasilinear elliptic systems. Our main tool is a recent three critical points theorem of Averna and Bonanno [D. Averna, G. Bonanno, A three critical points theorem and its applications to the ordinary Dirichlet problem, Topol. Methods Nonlinear Anal. 22 (2003) 93–104].