On account of uncertainty and complexity of environments, it is more suitable to express their assessed value by means of hesitant fuzzy information for decision makers. In this paper, we establish a new group decision-making (GDM) model with incomplete hesitant fuzzy preference relations (HFPRs) based on mathematical programming approach. Firstly, based on the multiplicative consistency of incomplete HFPR, a mathematical programming model is established to obtain multiplicative consistent fuzzy preference relation (FPR) from a given incomplete HFPR. Following this, experts are assigned with weights according to their consistency degree. Subsequently, a group consensus reaching process algorithm is constructed based on the obtained multiplicative consistent FPRs. Correspondingly, a GDM model is further established. Finally, a medical decision application is studied to present the practicability and effectiveness of the proposed method.