Shape memory polymers (SMPs) are currently one of the most attractive smart materials expected to replace traditional shape memory alloys and ceramics (SMAs and SMCs, respectively) in some fields because of their unique properties of high deformability, low density, easy processing, and low cost. As one of the most popular SMPs, shape memory polyurethane (SMPU) has received extensive attention in the fields of biomedicine and smart textiles due to its biocompatibility and adjustable thermal transition temperature. However, its laborious synthesis, limitation to thermal response, poor conductivity, and low modulus limit its wider application. In this work, biocompatible poly(ε-caprolactone) diol (PCL-2OH) is used as the soft segment, isophorone diisocyanate (IPDI) is used as the hard segment, and glycerol (GL) is used as the crosslinking agent to prepare thermoset SMPU with a thermal transition temperature close to body temperature for convenient medical applications. The effects of different soft-chain molecular weights and crosslinking densities on the SMPU’s properties are studied. It is determined that the SMPU has the best comprehensive performance when the molar ratio of IPDI:PCL-2OH:GL is 2:1.5:0.33, which can trigger shape memory recovery at body temperature and maintain 450% recoverable strain. Such materials are excellent candidates for medical devices and can make great contributions to human health.