A　discrete　modified　Leslie-Gower　prey-predator　model　considering　the　effect　of　fear　on　prey　species　is　proposed　and　studied　in　this　paper.　First,　we　discuss　the　existence　of　equilibria　and　the　local　stability　of　the　model.　Second,　we　use　the　iterative　method　and　comparison　principle　to　obtain　the　set　of　conditions　which　ensures　the　global　attractivity　of　positive　equilibrium　point.　The　results　show　that　prey　and　predator　can　coexist　stably　when　the　intrinsic　growth　rates　of　both　prey　and　predator　are　maintained　within　a　certain　range.　Then,　we　study　the　global　attractivity　of　the　boundary　equilibrium　point.　Our　results　suggest　that　when　the　intrinsic　rate　of　prey　is　small　enough　or　the　fear　factor　is　large　enough,　the　prey　will　tend　to　go　extinct,　while　the　predator　can　survive　stably　due　to　the　availability　of　other　food　sources.　Subsequently,　we　discuss　flip　bifurcation,　transcritical　bifurcation　at　the　equilibria　of　the　system,　by　using　the　center　manifold　theorem　and　bifurcation　theory.　We　find　that　system　changes　from　chaotic　state　to　four-period　orbit,　two-period　orbit,　stable　state,　and　finally　prey　species　will　be　driven　to　extinction,　while　predator　species　survive　in　a　stable　state　for　enough　large　birth　rate　of　prey　species　with　the　increasing　of　fear　effect.　Finally,　we　verify　the　feasibility　of　the　main　results　by　numerical　simulations,　and　discuss　the　influence　of　the　fear　effect.　The　results　show　that　the　fear　effect　within　a　certain　range　can　enhance　the　stability　of　the　system.