Abstract: The structural response under ambient excitation is a stochastic process. The response changes with damage, so does the stochastic process. From this fact, the parameters demonstrating the characteristics of stochastic process can be recommended to evaluate the state of structure. Entropy is a suitable measurement of stochastic process uncertainty, either for Gaussian or non-Gaussian for distributed data . According to those principles, the concept of singular-spectrum cross-entropy is proposed based on the techniques of phase space reconstruction and singular value decomposition. It is then used as an index for damage diagnosis under ambient excitation. The method was tested on the benchmark model designed by ASCE task group, the response of which was acquired by NExT technique. The embedding dimension of phase space was obtained with false neighbor technique. The influences of operational conditions and noise on diagnosis were analyzed, the results of which confirm the effectiveness and robustness of the proposed method.