In order to solve the dynamic evaluation problem of cloud computing security, a method named interval-valued hesitant fuzzy grey compromise relation analysis for accurately evaluating the security of cloud computing was proposed. Firstly, a new interval-valued hesitant fuzzy distance formula was defined to measure the distance between two interval-valued hesitant fuzzy sets. Then, two new interval-valued hesitant fuzzy normalization formulas were constructed to solve the different dimensions of attributes. Meanwhile, the concept of grey compromise relation degree was put forward to consider all the expert opinions and solve the situation when the attributes have conflicts. On the basis of this, a new interval-valued hesitant fuzzy grey compromise relation analysis method was presented to evaluate the security of cloud computing. The analysis results show that the proposed method is feasible, and its scientific and effective characters are proved by comparing with the existed interval-valued hesitant fuzzy multiple attribute decision making literatures.