This　paper　discusses　a　discrete　SIR　epidemic　model　with　immunity.　The　basic　reproduction　number　is　established.　It　is　shown　that　the　disease-free　equilibrium　is　globally　stable　if　the　basic　reproduction　number　is　less　than　one,　and　the　positive　equilibrium　exists　if　the　basic　reproduction　number　is　more　than　one.　The　global　stability　of　the　positive　equilibrium　is　obtained　in　the　case　where　the　immunization　rate　is　equal　to　the　removed　rate.