Recently, Xiong et al. have proposed a secure data self-destructing scheme [IEEE TCC, vol. 2, no. 4, pp. 448- 458, 2014] in cloud computing. The scheme aims to solve some important security problems by supporting user-defined authorization period and by providing fine-grained access control during the period. The sensitive data will be securely self-destructed after a user-specified expiration time. In this note, it shows that the scheme is awed because its decryption mechanism is incorrect. The consistency between encryption mechanism and decryption mechanism is not kept. We also show that it seems difficult to revise its decryption mechanism.