Droplet　dynamics　in　microfluidic　applications　is　significantly　influenced　by　surfactants.　It　remains　a　research　challenge　to　model　and　simulate　droplet　behaviour　including　deformation,　breakup　and　coalescence,　especially　in　the　confined　microfluidic　environment.　Here,　we　propose　a　hybrid　method　to　simulate　interfacial　flows　with　insoluble　surfactants.　The　immiscible　two-phase　flow　is　solved　by　an　improved　lattice　Boltzmann　colour-gradient　model　which　incorporates　a　Marangoni　stress　resulting　from　non-uniform　interfacial　tension,　while　the　convection-diffusion　equation　which　describes　the　evolution　of　surfactant　concentration　in　the　entire　fluid　domain　is　solved　by　a　finite　difference　method.　The　lattice　Boltzmann　and　finite　difference　simulations　are　coupled　through　an　equation　of　state,　which　describes　how　surfactant　concentration　influences　interfacial　tension.　Our　method　is　first　validated　for　the　surfactant-laden　droplet　deformation　in　a　three-dimensional　(3D)　extensional　flow　and　a　2D　shear　flow,　and　then　applied　to　investigate　the　effect　of　surfactants　on　droplet　dynamics　in　a　3D　shear　flow.　Numerical　results　show　that,　at　low　capillary　numbers,　surfactants　increase　droplet　deformation,　due　to　reduced　interfacial　tension　by　the　average　surfactant　concentration,　and　non-uniform　effects　from　non-uniform　capillary　pressure　and　Marangoni　stresses.　The　role　of　surfactants　on　the　critical　capillary　number　(Ca-cr)　of　droplet　breakup　is　investigated　for　various　confinements　(defined　as　the　ratio　of　droplet　diameter　to　wall　separation)　and　Reynolds　numbers.　For　clean　droplets,　Cacr　first　decreases　and　then　increases　with　confinement,　and　the　minimum　value　of　Ca-cr　is　reached　at　a　confinement　of　0.5;　for　surfactant-laden　droplets,　Ca-cr　exhibits　the　same　variation　in　trend　for　confinements　lower　than　0.7,　but,　for　higher　confinements,　Ca-cr　is　almost　a　constant.　The　presence　of　surfactants　decreases　Ca-cr　for　each　confinement,　and　the　decrease　is　also　attributed　to　the　reduction　in　average　interfacial　tension　and　non-uniform　effects,　which　are　found　to　prevent　droplet　breakup　at　low　confinements　but　promote　breakup　at　high　confinements.　In　either　clean　or　surfactant-laden　cases,　Ca-cr　first　remains　almost　unchanged　and　then　decreases　with　increasing　Reynolds　number,　and　a　higher　confinement　or　Reynolds　number　favours　ternary　breakup.　Finally,　we　study　the　collision　of　two　equal-sized　droplets　in　a　shear　flow　in　both　surfactant-free　and　surfactant-contaminated　systems　with　the　same　effective　capillary　numbers.　It　is　identified　that　the　non-uniform　effects　in　the　near-contact　interfacial　region　immobilize　the　interfaces　when　two　droplets　are　approaching　each　other　and　thus　inhibit　their　coalescence.