Shape memory polymers (SMPs) are novel kinds of smart materials whose shape can be changed in external conditions such as heat stimulus. Due to their excellent structural versatility and high elastic strain, they have important applications in the field of biomaterials. Here, a series of amorphous shape memory polymer materials are prepared and their shape memory properties and glass transition temperature (Tg) are also investigated. A special kind of epoxy polymer, whose shape can be changed at around physiological temperature, is synthesized by regulating the crosslinking density and introducing flexible aliphatic epoxy chains. The shape memory function of this epoxy polymer is studied by deformation test. In addition, to explore their application in the field of biomedical materials, the biocompatibility of the materials are evaluated, including the effects on the erythrocyte hemolysis rate and cell activity. The experimental results show that this kind of epoxy polymer has good shape memory function and biocompatibility.