We study the flow behaviors of emulsion droplets in constricted capillaries using a surfactant Lattice Boltzmann model. We first establish the model by introducing a surfactant component into the pseudopotential multiphase model and characterizing the amphiphilic structure using dipoles. Then we study the flow of emulsion droplets in single or parallel capillaries. The simulations show that single droplet can pass through single throat in three ways, i.e., passing directly, passing with deformation, and snap-off. Multiple droplets may flow through the capillary with coalescence, and can also block the throat by adsorption or bridging, which may induce upstream flow caused by buoyancy. There is a “trap effect” when emulsions flow through parallel throats, and the droplet could be pinched off by obstacles, while the surfactants can inhibit the droplet breakup due to Marangoni effect. The simulations present detailed flow behaviors at pore scale and provide new insights for emulsion flow modeling.