System reliability has been a major concern since the beginning age of the electronic digital computers. One of the modest ways of increasing reliability is to design fault-tolerant system. This paper propose a construction mechanism of fault-tolerant system for the general graph topology. This system has several spare nodes. Up to date, fault-tolerant system design is applied only to loop and tree networks. But they are very limited cases. New algorithm of this paper tried to have a capability which can be applied to any kinds of topologies without such a many restriction. the algorithm consist of several steps : minimal diameter spaning tree extraction step, optimal node decision step, original connectivity restoration step and finally redundancy graph construction step.