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This paper aims to develop a new group decision making (GDM) approach with intuitionistic multiplicative preference relations (IMPRs) by considering the consistency and consensus. Using the distance between a given IMPR and its corresponding underlying consistent IMPR, the concept of acceptably consistent IMPR is introduced, then an automatic algorithm is designed to repair the inconsistent IMPR to be of acceptable consistency. Meanwhile, each decision maker's consensus level is evaluated by the deviation between his/her individual IMPR and the group IMPR, and another algorithm for reaching acceptable level of consensus is provided. Moreover, the consensus improving process can guarantee that the modified IMPRs still be acceptably consistent, then the normalized intuitionistic multiplicative priority weight vector can be obtained from a mathematical programming model. A step-by-step algorithm based on the consistency and consensus of IMPRs is offered. Finally, two examples and the corresponding comparative analyses are presented to demonstrate the effectiveness of the proposed method.