In this paper we discuss the following nonlinear degenerate parabolic systems u;=△a;(u;)+b;(x,t,u;)Du;+f;(x,t,u)for i = 1,2, …, m and u = (u;,…, u;) is a vector function, with Dirichlet boundary condition. Under some structure conditions on a;,b;and f;and initial data u;∈Li(Ω) for some pi>p;= 1,2,…,m, the result on existence and uniquence of global solution is established.