A method of damage identification based on the flexural curvature polynomials curve fitting was presented and the method was then used to study the damage of thin plate structures. The modal shapes and natural frequencies of the damaged thin plate were obtained by the modal analysis using the finite element software ANSYS, and the flexibility curvatures in X-direction and Y-direction were provided. Then they were fitted with polynomial curves in the direction of X and Y axis. Based on the difference between the fitting values and the original values, a new damage index was proposed. The numerical results show that the method based on the flexibility curvature polynomial curve fitting can identify the damage position of the plate more accurately than the methods which only use the flexibility curvature matrix. Comparing with other methods, in the method it is not necessary to have the knowledge about the vibration modes of the original structure, so it can identify the damage cases where it is difficult to get the modal data in healthy state of the structure.