For multi-attribute group decision making (MAGDM) problem, there exist inter-dependent or interactive phenomena among criteria or preference of decision makers, therefor it is not suitable for us to aggregate them by conventional aggregation operators based on additive measures. In this paper based on fuzzy measures an interval-valued Pythagorean fuzzy Choquet integral geometric (IVPFCIG) operator is investigated for multiple criteria group decision making. First, some operational laws on interval-valued Pythagorean fuzzy numbers (IVPFNs) are introduced. Then an interval-valued Pythagorean fuzzy Choquet integral geometric (IVPFCIG) operator is proposed. Moreover, some of its properties are given and discussed in detail. Then Choquet integral-based distance between interval-valued Pythagorean fuzzy numbers is defined. Combining the IVPFCIG operator with Choquet integral-based distance, an extension of TOPSIS method is developed to deal with multi-attribute interval-valued Pythagorean fuzzy group decision making problems. Finally a numerical example is used to illustrate the developed procedures.