In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $${array{-{Delta}_pu-{Delta}_qu={lambda}V(x)|u|^{r-2}u+frac{2{alpha}}{alpha+eta}|u|^{alpha-2}u|v|^{eta},;x{in}{Omega}\-{Delta}p^v-{Delta}q^v={ heta}V(x)|v|^{r-2}v+frac{2eta}{alpha+eta}|u|^{alpha}|v|^{eta-2}v,;x{in}{Omega}\u=v=0,;x{in}{partial}{Omega}}$$ where ${Omega}$ is a bounded domain in $R^N$, ${lambda}$, ${ heta}$ > 0, and 1 < ${alpha}$, ${eta}$, ${alpha}+{eta}=p^*=frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${Delta}_su=div(|{ abla}u|^{s-2}{ abla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.