When a small amount of polymer is added to a liquid capillary bridge between two solid surfaces under steady shear, the effective friction of the receding contact line increases. The critical factor of the determination of the contact line friction is the local polymer concentration near the contact line, which alters the liquid–solid interfacial tension. According to the modified equation of the molecular kinetic theory for polymer solutions, the capillary force has static and dynamic contributions from the local polymer concentration. We show that adding polymer to the solution leads to a large friction coefficient due to the high local polymer concentration. This work also finds that a capillary bridge under steady shear shares the contact line dynamics with an impacted droplet. The origin of the rebound suppression of a dilute polymer solution droplet is, therefore, the increased friction on a retracting contact line by strongly surface-adsorbed polymer molecules.