The origin of rebound suppression of an impacting droplet by a small amount of polymer additive has been tentatively explained by various physical concepts including the dynamic surface tension, the additional energy dissipation by non-Newtonian elongational viscosity, the elastic force of stretched polymer, and the additional friction on a receding contact line. To better understand the role of polymer on a molecular level, we performed multi-body dissipative particle dynamics simulations of droplets impacting on solvophobic surfaces. The rebound suppression is achieved by the elastic force of stretched polymer during the hopping stage, and the additional friction on the contact line during the retraction stage. Both slow-hopping and slow-retraction mechanisms coexist in a wide range of simulation parameters, but the latter is prevailing for large droplets, and for the strong attraction strength between polymer and surface. The increased polymer adsorption, which maybe achieved by a higher polymer concentration or a larger molecular weight, stimulates both mechanisms. Also, the molecular evidence of the additional friction on the receding contact line is shown from the relation between the contact angle and the contact line velocity where the slope of the fitted line is an indication of the additional friction.