A series of polyurethanes (PUs) based on poly (tetramethylene glycol) (PTMG), poly (ethylene adipate) (PEA) diol, polycaprolactone (PCL) diol and castor oil (CO) were synthesized. The tensile, damping and thermal properties were studied systematically in terms of the composition and isocyanate index (R). Results showed that when R is 2, the PUs exhibit a relatively high tensile strength more than 30 MPa. The PTMG-PU, PCL-PU and PEA-PU show high elongation at break compared to the cross-linked CO-PU. When R is 1.5, tensile strengths decrease compared to R is 2. But, the elongations of PTMG-PU, PCL-PU and CO-PU increase. DMA analysis showed that the glass transition temperature (Tg) is increasing as the sequence of PTMG-PU, PCL-PU, PEA-PU and CO-PU. The Tg of CO-PU is as high as 60.6 °C when R is 1.5 and 93.4 °C when R is 2. The Tg ranges of the other linear PUs are between −50 and −12 °C. The damping temperature ranges of these PUs are relatively broad. Further, TG results showed the start degradation temperatures of them are approx 260 °C. These results show a good guidance to select a kind of PU when prepare the PU-polymer composites for given properties.