A polymer solution with a transient network structure due to the entanglement of long chain molecules exhibits a viscoelastic behavior when it flows through a tortuous and diverging/converging channel in porous media. A constitutive equation is first developed to represent the viscoelastic behavior of polymer solutions in this article. Then a 3D viscoelastic polymer flooding model is established to examine the effect of elasticity of polymers on EOR (enhanced oil recovery). The model is validated in comparison with laboratorial coring data. The simulated results show that the oil recovery of viscoelastic polymer flooding can be enhanced by larger displacement efficiency due to its microscopic roles. In the meanwhile, the injection pressure required increases correspondingly if the elastic effect is significant. Relaxation time as a major characteristic parameter of viscoelastic polymer plays a decisive role, and therefore the HPAM (partially hydrolyzed polyacrylamide) with evident elastic property is recommended in chemical flooding.