Abstract: A new nonlinear viscoelastic constitutive relation baced on the three-dimensional nonlinear viscoelastic constitutive relations by Stieltjes convolution and the elastic recovery correspondence principle in the form of three-dimension constitutive relation is proposed in this paper.The new nonlinear viscoelastic constitutive relation is applied to forecast the stress respons of polypropylene single-axis tension to different strain’s rates in the tests.The fact that the nonlinear viscoelastic constitutive relation based on the elasticity recovery correspondence principle can be used to describe the constitutive behavior of polymer,a class of nonlinear viscoelastic material,is verified by the theoretic calculations.