Polyurethane is an important biomaterial with wide applications in biomedical engineering. Here, we report a new method to make an azido-functionalized polyurethane prepolymer with no need of postmodification. This prepolymer can easily form stable porous elastomers through click chemistry for cross-linking, instead of using a toxic polyisocyanate. The mechanical properties can be modulated by simply adjusting either the prepolymer concentrations or azido/alkyne ratios for cross-linking. Young's modulus therefore varies from 0.52 to 2.02 MPa for the porous elastomers. When the azido-functionalized polyurethane elastomer is made with a compact structure, Young's modulus increases up to 28.8 MPa at 0-15% strain. The strain at break reaches 150% that is comparable to the commercially resourced Nylon-12. Both the porous and compact elastomers could undergo reversible elastic deformations for at least 200 and 1000 cycles, respectively, within 20% strain without failure. The material showed a considerable stability against erosion in a basic solution. In vivo biocompatibility study demonstrated no degradation by subcutaneous implantation in mice over 2 months. The implant induced only a mild inflammatory response and fibrotic capsule. This material might be useful to make elastomeric components of biomedical devices.