The stability analysis for the fuzzy logic controller (FLC) has widely been reported. Furthermore many research in the FLC has been introduced to decrease the number of parameters representing the antecedent part of the fuzzy control rule. In this paper we briefly explain a single-input fuzzy logic controller (SFLC) or simple-structured FLC which uses only a single input variable. And then we analyze that it is absolutely stale based on the sector bounded condition. We also show the feasibility of the proposed stability analysis through a numerical example of a mass-damper-spring system.