In　this　paper,　a　Leslie-Gower　model　with　weak　Allee　effect　on　prey　and　fear　effect　on　predator　is　proposed.　Compared　with　the　case　without　fear　effect　on　predator,　the　new　model　undergoes　richer　dynamic　behaviors　such　as　saddle-node　bifurcation,　Hopf　bifurcation　and　Bogdanov-Takens　bifurcation.　Also,　different　from　the　strong　Allee　effect　on　prey,　the　system　with　weak　Allee　effect　has　bistable　attractors　which　are　a　largely　stable　limit　cycle　and　a　stable　positive　equilibrium,　two　stable　equilibria,　or　a　stable　limit　cycle　and　a　stable　trivial　equilibrium.　When　the　Allee　effect　coefficient　is　intermediate,　fear　effect　on　the　predator　can　protect　the　prey　and　the　predator　from　being　extinguished.　The　results　in　this　paper　can　be　seen　as　a　complement　to　those　in　the　literatures　about　the　Leslie-Gower　model　with　Allee　effect　and　fear　effect.