By using the interval grey language to describe the uncertain information in the evaluation of packaging enterprise’ innovation ability, based on the analysis of the multi-criteria group decision-making issue considering the interrelationship of individual criterion through the Power operator, an evaluation model of the packaging enterprise’s innovation ability was built. Firstly, by combining the concepts of interval grey linguistic variables and Power operator, a series of operators such as interval grey linguistic power hybrid averaging operator was proposed. Then, a multi-criteria group decision-making model with the criterion values taking the form of interval grey linguistic variables was constructed. Finally, an illustrative example of the evaluation of paper packaging enterprise’ technological innovation capability was used to demonstrate the feasibility and usefulness of the proposed method.