Resistive　switching　(RS)　memristor　has　been　widely　used　in　the　in-memory　computation　systems.　Due　to　the　strong　information　processing　capability　and　low　area　cost　of　the　ternary　logic,　the　development　of　the　three-state　RS　memristor　was　promoted.　Here,　we　demonstrate　a　three-state　RS　phenomenon　on　Pt/BiFeO3/SrRuO3　structure.　After　applying　a　positive　voltage　to　the　thin　film　for　a　period,　an　abrupt　RS　effect　occurs,　where　the　three-state　RS　behavior　can　be　obtained.　By　analyzing　the　conduction　mechanisms　of　the　current-voltage　curves　and　the　behavior　of　the　capacitance-voltage　curves,　the　three-state　storage　capability　of　the　memristor　can　be　ascribed　to　the　movement　of　oxygen　vacancies　and　the　trapping/detrapping　of　charge　carriers　at　the　interface.　The　ternary　OR　logic　gate　was　also　designed　with　three　steps　by　using　only　one　memristor.