With respect to that the traditional geometric average operator in dynamic multiattribute decision making method with integrated data expressed in intervalvalued intuitionistic fuzzy number (IVIFN) fails to consider the relationships between the integrated data, and the overall precision of the final decision result is not high enough, an improved multiattribute decision making method based on the new proposed dynamic power weighted geometric average (PWGA) operator of IVIFN is proposed. The ability to display nonmonotonic behavior provides one of the useful features of these operators to establish a connection between the integrated data. Firstly, the PWGA operator of real numbers is extended to PWGA of IVIFN and a proof that the final collective value is still a IVIFN is given as well. Besides, a dynamic intervalvalued intuitionistic fuzzy PWGA (DIIFPWGA) operator is proposed at the same time. Thereby, applying the DIIFPWGA operator, the individual overall evaluation values at each time point of alternatives are then integrated into collective ones, which are used to rank the alternatives based on the score function and accuracy function of IVIFN. Finally, a numerical example is given to illustrate and validate the proposed approaches.