This study aims to develop a sensitivity-based approach to identify the local damages in axially functionally graded beams. An objective function is established by minimizing the differences between the calculated and measured natural frequencies

and acceleration responses of the beam. An iterative optimization procedure is conducted by linearizing the objective function based on the penalty function method. A hybrid sensitivity matrix is constructed and used in the finite element model updating. The advantage of the present method lies in only the first several natural frequencies

and a few number of acceleration responses are needed in the identification. A single span simply supported beam and a multi-span beam are studied as two numerical examples to illustrate the correctness and efficiency of the proposed method. Good identified results can be obtained from the short time histories of a few number of measurement points and the first several natural frequencies.