Grafted isopropyl groups were used to control the molecular interactions between polyurethane (PU) copolymers, and their effect on the tensile properties of PU was investigated. The grafted isopropyl groups were selected to interrupt the molecular interactions and disturb the close contact between PU chains through its branched structure, and thus improve the low-temperature recovery while maintaining the high tensile properties and the shape recovery at ambient temperature. The grafted isopropyl groups made a difference to the phase separation of the hard and soft segments in the PU structure, as determined by IR and DSC. The crosslink density and viscosity experienced an unusual increase with the increase in isopropyl content owing to crosslinking by the grafting reagent. The shape recovery and retention remained high even with the grafted isopropyl groups. Finally, the effect of the isopropyl groups on low-temperature recovery was compared with that of the linear PU, and the reason for the flexibility is discussed.