Summary: In this paper, we investigate the hesitant fuzzy multiple attribute decision making with incomplete weight information. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the hesitant fuzzy weighted averaging (HFWA) operator to aggregate the hesitant fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score function. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.