Ship design process requires lots of complicated analyses for determining a large number of design variables. Due to its complexity, the process is divided into several tractable designs or analysis problems. The interdependent relationship requires repetitive works. This paper employs collaborative optimization (CO), one of the multidisciplinary design optimization (MDO) techniques, for treating such complex relationship. CO guarantees disciplinary autonomy while maintaining interdisciplinary compatibility due to its bi-level optimization structure. However, the considerably increased computational time and the slow convergence have been reported as its drawbacks. This paper proposes the use of an approximation model in place of the disciplinary optimization in the system-level optimization. Neural network classification is employed as a classifier to determine whether a design point is feasible or not. Kriging is also combined with the classification to make up for the weakness that the classification cannot estimate the degree of infeasibility. For the purpose of enhancing the accuracy of a predicted optimum and reducing the required number of disciplinary optimizations, an approximation management framework is also employed in the system-level optimization.