The role of surfactants in the flow of a droplet driven by a pressure gradient through a constricted microchannel is simulated by using our recently developed lattice Boltzmann method. We first study the surfactant role on a droplet flowing through a microchannel with a shrunken square section under different surfactant concentrations and capillary numbers (i.e., imposed pressure gradients). As the surfactant concentration increases, the droplet flow regime first changes from the flow regime I of the droplet getting stuck at the entrance of the constricted channel to the flow regime II of the droplet flowing through the constricted channel with breakup, and then to the flow regime III of the droplet flowing through the constricted channel without breakup. As the capillary number increases, the surfactant role on the number of mother droplets breaking up and the time of mother droplets completely flowing through the constricted section tend to decrease, suggesting that the surfactant effects are gradually weakened. Then, a phase diagram describing how the surfactant concentration and capillary number affect the droplet flow regime is presented. As the surfactant concentration increases, the critical capillary number that distinguishes droplet flow regimes I from II gradually decreases, while the critical capillary number that distinguishes droplet flow regimes II from III first increases and then decreases.