In this paper, an improved NSGA - II algorithm is proposed based on the principal curve modeling for solving the expensive interval multi-objective optimization with unknown objective function. Firstly, the proposed algorithm builds a K principal curve using the population data of the manifold distribution in decision space. Then, a new offspring is generated through interpolation and extension according to the built K principal curve, and the proposed strategy of offspring generation is more efficient than that of random offspring generation in the genetic algorithm. Finally, because of the absence of the crowding distance in objective space, the closest solutions before and after the candidate solution can be found based on the built K principal curve, so the solutions with same sequence are screened by crowding distance in decision space, thus the NSGA-II is improved.