Polymer flooding is a promising chemical enhanced oil recovery method, which realizes more efficient extraction in porous formations characterized with nanoscale porosity and complicated interfaces. Understanding the molecular mechanism of viscoelastic polymer enhanced-oil-recovery in nanopores is of great significance for the advancement of oil exploitation. Using molecular dynamics simulations, we investigated the detailed process of the viscoelastic polymer displacing oil at the atomic scale. We found that the interactions between polymer chains and oil provide an additional pulling effect on extracting the residual oil trapped in dead-end nanopores, which plays a key role in increasing the oil displacement efficiency. Our results also demonstrate that the oil displacement ability of polymer can be reinforced with the increasing chain length and viscoelasticity. In particular, polymer with longer chain length exhibits stronger elastic property, which enhances the foregoing pulling effect. These findings can help to enrich our understanding on the molecular mechanism of polymer enhanced-oil-recovery and provide guidance for oil extraction engineering.