The　dynamic　behavior　of　compound　droplets　on　the　wall　of　a　rectangle　channel　by　the　action　of　an　imposed　shear　flow　is　simulated　using　our　developed　three-dimensional　front-tracking　method　combined　with　generalized　Navier　boundary　condition.　The　validity　of　the　present　method　was　confirmed　by　comparing　results　of　the　compound　droplet　spreading　under　gravity　force　with　analytical　solutions.　To　determine　the　physical　condition　required　for　detaching/pinching-off　the　compound　droplet,　we　have　performed　a　large　number　of　simulations　with　varying　capillary　numbers　of　two　interfaces　and　obtained　a　phase　diagram　of　compound　droplets　on　solid　surface　in　shear　flow.　The　deformation　and　motion　of　the　compound　droplet　including　its　contact　line　motion　are　investigated.　It　is　found　that　the　behavior　of　the　compound　droplet　is　controlled　by　two　dimensionless　parameters,　the　capillary　numbers　of　the　outer　interface　and　the　inner　interface.　Moreover,　we　also　analyze　the　deformation　and　migration　of　the　inner　droplet　and　discuss　its　effect　on　the　compound　droplet.　The　simulation　demonstrate　that　the　lateral　migration　of　the　small　inner　droplet　could　accelerates　the　pinch-off　process　and　the　large　inner　droplet　could　promote　the　detachment　for　a　moderate　capillary　number　of　the　outer　interface.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.