The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals.We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations.The first result shows only the existence.And the second one shows the existence and uniqueness result based on the first result,but the uniqueness requires some compatibility condition.