A decision method of integrating the prospect theory with TOPSIS is proposed for multi-attribute decision-making, where the attribute weights are unknown and attribute values are in the form of hesitant fuzzy number. Considering the different attitudes of decision makers toward index sets, An approach to determine the weights of attribute by the entropy method based on the hesitant fuzzy entropy is proposed. The prospect value function of the hesitant fuzzy number is defined by introducing the psychological risk factors of decision makers into hesitant fuzzy multi-attribute decision-making, and the hesitant fuzzy decision-making matrix is converted to the value matrix based on which the ratio of gains to losses of the alternatives is calculated. Finally, TOPSIS method is used to rank all the alternatives and a numerical example is provided to illustrate the effectiveness of the proposed method.