A new type of contra-rotating propellers (CRP) system has been developed through the cooperative research work of five shipbuilding companies (HZ, KHI, MES, NKK, SHI). This paper describes a design system for an optimum CRP, which is one of the numerous fruits obtained from the cooperative work. The optimum design system is composed of three theoretical programs, i. e. (1) Design program of optimum CRP, (2) Steady lifting surface program of CRP, (3) Unsteady lifting surface program of CRP. In the former part of this paper, these theoretical programs will be discussed, and the design system supported by these theoretical programs will be verified by comparing calculated results with experiments in the latter part.