In view that the attribute value is intuitionistic fuzzy numbers in multi-attribute decision making problems, we present a new TOPSIS method of multi-attribute decision-making. Firstly, we employ the intuitionistic fuzzy cloud to describe all attribute values of the alternatives, and calculate the expectations, entropy and hyper entropy of the alternatives. Secondly, we construct the decision matrix of numerical characteristics, and obtain the corresponding positive and negative ideal solutions. Finally, we calculate the distance between the numerical characteristics and the positive and negative ideal solutions, and get a composite closeness coefficient, thus obtaining the optimal decision results. The rationality and validity of the presented method are verified through numerical examples.