For constrained multi-objective optimization problems with interval numbers, a kind of interactive multi-attribute decision-making NSGA-II is proposed. In this algorithm, nonlinear optimization problems are transformed into linear ones. P dominance relationship is defined to get the rank values of individuals and interval crowding distance is presented to distinguish the quality of the individuals with the same rank value. A constrained elite strategy is used to remove those individuals that do not satisfy the constraint from the population. A multi-attribute decision-making model(DMM) is built, which regards the selected individuals as the alternatives set, the objective function as the attributes set, and the preference of each objective function as the attribute weights. In the process of evolution, an interactive NSGA-II incorporated with DMM is proposed to obtain satisfactory solutions which conform to the decision-makers preference. Simulation results show the feasibility and correctness of the proposed method.