Gradually　expanding　gap　in　the　outlet　of　the　Roots　blower　can　effectively　reduce　the　backflow　impact　and　the　noise　of　the　blower.　The　working　principle　for　the　Roots　blower　with　the　gradually　expanding　gap　is　investigated　in　this　paper.　And　the　mathematical　modelling　for　backflow　is　proposed.　Numerical　methods　are　given　to　solve　the　outlet　gap　size.　The　performance　parameters　of　different　dimension　gap　are　compared.　The　outlet　flow　field　in　Roots　blower　with　gradually　expanding　gap　is　simulated　by　means　of　CFD　simulation.　Finally,　the　correctness　of　the　numerical　solution　is　verified.