With respect to the multi-attribute decision making problem with Pythagorean uncertain linguistic variables, in which attribute weights and expert weights are completely unknown, an extended VIKOR method is proposed. Firstly, the concept of Pythagorean uncertain linguistic variables is defined. Combining with the concept of linguistic scale functions, the operational laws, comparison method and Hamming distance of Pythagorean uncertain linguistic variables are also proposed to accommodate different semantic situations. Then, an objective attribute weight determination method is proposed to determinate the attribute weights based on the Pythagorean uncertain linguistic entropy measure, and an objective expert weight determination method is also proposed to determine the weight of experts with respect to each attribute by calculating the similarity degree among evaluation values in which the attribute values are expressed as Pythagorean uncertain linguistic variables. Based on the above research, an extended VIKOR method is proposed to solve Pythagorean uncertain linguistic multi-attribute group decision making problems. Finally, an example of domestic airline service quality evaluation is provided to demonstrate the effectiveness and feasibility of the proposed method.