An approach based on multi-objective optimization of attribute weights is proposed to deal with the hesitant fuzzy multiple attribute decision making problem with attribute weights completely unknown. Firstly, the mean and variance for attribute values, and the correlation coefficients between attributes are computed. An optimization model is constructed to determine the attribute weights. Then, the similarity degree between each alternative and the hesitant fuzzy positive ideal point is obtained to rank the alternatives. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed method.