The invention is directed to a biodegradable tissue-adhesive polyurethane polymer comprising at least one amorphous segment and at least one polyurethane segment, wherein at least one of said polyurethane segment comprises a tissue-reactive functional group. A further aspect of the invention is directed to biodegradable tissue-adhesive medical devices, based on the polyurethane polymer, having the structure of a sheet, foam, stent, tube or gel. The polyurethane polymer and the device can be used in medical application.