Recently proposed q-rung orthopair fuzzy set (q-ROFS) is a powerful and effective tool to describe fuzziness, uncertainty and vagueness. The prominent feature of q-ROFS is that the sum and square sum of membership and non-membership degrees are allowed to be greater than one with the sum of qth power of the membership degree and qth power of the non-membership degree is less than or equal to one. This characteristic makes q-ROFS more powerful and useful than intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS). The aim of this paper is to develop some aggregation operators for fusing q-rung orthopair fuzzy information. As the Muirhead mean (MM) is considered as a useful aggregation technology which can capture interrelationships among all aggregated arguments, we extend the MM to q-rung orthopair fuzzy environment and propose a family of q-rung orthopair fuzzy Muirhead mean operators. Moreover, we investigate some desirable properties and special cases of the proposed operators. Further, we apply the proposed operators to solve multi-attribute group decision making (MAGDM) problems. Finally, a numerical instance as well as some comparative analysis are provided to demonstrate the validity and superiorities of the proposed method.