In our daily life, we could be confronted with numerous multiple attribute group decision making (MAGDM) problems. For such problems we designed a model which employs probabilistic linguistic MABAC (multi-attributive border approximation area comparison) based on the cumulative prospect theory (CPT-PL-MABAC) method to solve the MAGDM. The CPT-PL-MABAC method can take experts’ psychological behaviour and preferences into consideration. Furthermore, we utilize the combined weight consisting of subjective weight and objective weight. The objective weight is acquired by the entropy method. Additionally, the concrete calculating steps of CPT-PL-MABAC method are proposed to solve the MAGDM for selecting the optimal location of express distribution centre. Also, a numerical example for location selection of express distribution centre is given as the justification of the usefulness of the designed method. Finally, we compare the designed model with the other three existing models, and summarize the advantages and shortcomings.