The interval-valued Pythagorean fuzzy set (IVPFS), as a new generalization of Pythagorean fuzzy set, which can be used to model complex uncertainty in the real multiple attribute group decision making (MAGDM) problems. This paper aims to develop some new operators for dealing with MAGDM issue with interval-valued Pythagorean fuzzy information, such as continuous interval-valued Pythagorean fuzzy ordered weighted quadratic averaging (C-IVPFOWQA) operator, weighted C-IVPFOWQA operator, ordered weighted C-IVPFOWQA operator and hybrid C-IVPFOWQA operator. The proposed operators not only improve the accuracy of decision making but also can reflect the decision makers’ risk preferences. Additionally, some desirable properties and special cases of these operators are investigated in detail. Later, we present a MAGDM method based on the hybrid C-IVPFOWQA operator. Finally, a numerical example is presented to illustrate the proposed method and comparison analysis is given to demonstrate the practicality and effectiveness.