Abstract: The concept of energy cross-entropy curvature matrix is proposed based on the structural vibration response, and it is used as a new index for arch dam damage detection under flow-induced vibration. The index is obtained with the structural vibration energy cross-entropy calculated twice before and after damage occurs by means of difference calculation, firstly to columns, and then to rows. Then the new indicator is constructed through principal diagonal elements based on the curvature difference matrix in energy cross-entropy. Numerical simulation examples indicate that the damage location and severity in structures, with single damage, multiple ones and lighter ones, can be detected efficiently through only the ambient excitation of arch dam. The results confirm the effectiveness of the proposed method.