The　compound　droplet　will　exhibits　much　more　complex　behavior　when　it　adheres　to　a　wall　under　flow.　Studying　the　influence　of　related　parameter　plays　an　important　role　in　the　manipulation　of　the　compound　droplet.　In　this　paper,　a　three-dimensional　numerical　method　involving　the　moving　contact　line　problem　is　developed　by　integrating　the　generalized　Navier　boundary　condition　into　the　front-tracking　method.　The　proposed　method　is　applied　to　study　the　effects　of　the　capillary　number　of　inner　and　outer　interface　and　the　volume　of　inner　droplet　on　the　deformation　and　motion　of　the　compound　droplet　adhering　to　the　wall　with　considering　the　contact　angle　hysteresis　effect.　It　found　that　the　compound　droplet　is　more　like　to　be　detached　or　pinched-off　by　the　flow　when　the　capillary　number　of　outer　interface　and　the　volume　of　inner　droplet　are　large　and　the　capillary　number　of　inner　interface　is　small.　Key　words　©　2017,　Science　Press.　All　right　reserved.