There are many aggregation operators and its applications have been developed up to date, but Pythagorean fuzzy Einstein weighted geometric (PFEWG) operator was not introduced. Therefore in this paper, we introduce Pythagorean fuzzy Einstein weighted geometric (PFEWG) operator. We also discuss some basic properties of the proposed operator, including idempotency, boundedness, and monotonicity. Finally, we apply the PFEWG operator to deal with multiple attribute group decision making problem under Pythagorean fuzzy information. For Pythagorean fuzzy Einstein weighted geometric (PFEWG) operator, we construct an algorithm for multiple attribute group decision making problem also. In the last we construct a numerical example also for multiple attribute group decision making problem