We　present　an　improved　phase-field　model　in　the　lattice　Boltzmann　scheme　to　investigate　the　droplet　dynamics　in　the　presence　of　soluble　surfactant.　The　phase-field　model　based　on　the　Ginzburg–Landau　free　energy　is　developed　in　which　the　immiscible　binary　fluid　interfacial　profile　is　independent　of　the　surfactant　concentration.　The　improved　model　is　validated　and　then　employed　to　study　the　surfactant　effect　on　single　droplet　deformation,　two　droplets　interactions　and　interactions　among　four　droplets　in　the　shear　flow.　The　results　show　that　the　increase　of　surfactant　concentration　promotes　droplet　deformation,　droplet　breakup　and　more　complex　droplet-droplet　interaction　compared　to　the　clean　droplet.　Moreover,　the　effects　of　capillary　number,　viscosity　ratio,　as　well　as　peclet　number　on　the　behavior　of　surfactant-covered　droplets　in　the　shear　flow　are　investigated.　The　results　indicate　that　the　droplet　Taylor　deformation　parameter　increases　with　the　increase　of　capillary　number　but　the　decrease　of　viscosity　ratio.　The　minimum　distance　between　two　interacting　droplets　enlarges　with　both　capillary　number　and　peclet　number.　©　2018　Elsevier　Ltd