Heterogeneous multi-attribute group decision-making (MAGDM), which is an extension of the MAGDM problems, deals with heterogeneous information formats. In this paper, a new method is proposed for heterogeneous MAGDM in which five kinds of information formats, involving intuitionistic fuzzy sets, triangular intuitionistic fuzzy numbers, trapezoidal intuitionistic fuzzy numbers, intervals, and real numbers, are used to represent the assessments of alternatives, the attribute weight information is incomplete and the decision-makers' weights are unknown. First, based on preference ranking organization method for enrichment evaluation (PROMETHEE), the net flows of alternatives are obtained. The attribute weights are determined reasonably through constructing a multi-objective program which is transformed into a single objective program to resolve. A conversion formula is defined to transform the net flows into the individual priorities. Then, the complete fuzzy preference relation for each DM is generated. The group priorities of alternatives are derived by a fuzzy linear programming (FLP) model. Therefore, an effect index is defined to obtain the weights of DMs, which can be used to adjust the group priorities. The ranking order of alternatives is derived by the adjusted group priority. Therefore, a new PROMETHEE-FLP method is put forward for heterogeneous MAGDM. Finally, a bank recruitment case is analyzed to demonstrate the effectiveness and application of the proposed method.