A squeeze film damper bearing comprises a bearing metal 2 for supporting a rotation shaft 1, a bearing casing 3 for covering the bearing metal 2 and a concentricity spring 4 between the bearing metal 2 and the bearing casing 3. The bearing casing 3 is provided at its inner periphery with a circumferential groove 3a for accommodating the spring. The spring 4 is made of an elongate steel sheet 4a and has a plurality of recesses 4b formed on a surface of the steel sheet 4a to provide a plurality of longitudinally aligned projections 4c on the other surface of the steel sheet. The steel sheet is bent into cylindrical shape. Each of the projections 4c has a curved surface with a generating line in parallel with the rotation shaft 1.