Based on the idea of linear programming technique for multidimensional analysis of preference (LINMAP), a novel three-phase LINMAP method is presented here for solving hybrid multi-criteria group decision making (MCGDM) with dual hesitant fuzzy (DHF) truth degrees and incomplete criteria weights information. Firstly, by simultaneously taking into account the difference between each alternative and all the others for the decision maker (DM), the difference of each alternative between the individual DM and the decision group, and the difference of each alternative between the individual DM and all the others, a tri-objective nonlinear programming model is created to determine the DMs' weights. Secondly, to derive the criteria weights, objective positive ideal solution (OPIS), and the objective negative ideal solution (ONIS), a new four-objective DHF mathematical programming model is established by minimizing inconsistency and maximizing consistency based on OPIS and ONIS, and a pair of parametric nonlinear programming models are technically established by unequal weighted summation approach for solving the four-objective DHF mathematical programming model, which can provide DMs with more agility and flexible space to change their preference. Thirdly, by considering the distances of each alternative from the OPIS and ONIS for individual DM and the decision group, a minimizing deviation optimal model is established to derive the group ranking order of alternatives. Finally, a new method is put forward for solving hybrid MCGDM with DHF truth degrees, and the validity and practicability of the proposed method is analyzed through a case of water quality monitoring system (WQMS) selection.