Pythagorean fuzzy set (PFS) can provide more flexibility than intuitionistic fuzzy set (IFS) for handling uncertain information,and PFS has been increasingly used in multi-attribute decision making problems.This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean (PULVHM) operator and VIKOR method.Firstly,we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable (PULV) and explore some properties of the operator.Secondly,taking the decision makers’ hesitation degree into account,a new score function is defined,and we further develop a new group decision making approach integrated with VIKOR method.Finally,an investment example is demonstrated to elaborate the validity of the proposed method.Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.