A　single　species　model　with　Allee　effect　and　density-dependent　birth　rate　x　d　ex　x　b　cx　x　a　dt　dx　(　)　is　proposed　and　studied　in　this　paper,　where　and　are　all　positive　constants.　Sufficient　conditions　which　ensure　the　system　admits　a　unique　globally　stable　positive　equilibrium　are　obtained.　Numeric　simulations　show　that　with　the　increasing　Alee　effect,　the　system　takes　a　much　longer　time　to　reach　its　stable　steady-state　the　solution,　however,　Allee　effect　has　no　influence　on　the　final　density　of　the　species.　©　2023　World　Scientific　and　Engineering　Academy　and　Society.　All　Rights　Reserved.