The sub-super solution method is used to research the existence of large solutions of the quasilinear elliptic

p-

Laplacian  system which is exponential. The existence and sufficient conditions of large solutions of the quasilinear elliptic

p-

Laplacian  system are discussed. The key point is to establish a set of inequalities which have solutions to get the sufficient conditions.The sufficient condition of the quasilinear elliptic

p-

Laplacian  system is obtanined

which is (a-p+1)(

e

-q+1)

<

bc.