In this paper, we present an immersed boundary method for simulating moving contact lines with surfactant. The governing equations are the incompressible Navier-Stokes equations with the usual mixture of Eulerian fluid variables and Lagrangian interfacial markers. The immersed boundary force has two components: one from the nonhomogeneous surface tension determined by the distribution of surfactant along the fluid interface, and the other from unbalanced Young's force at the moving contact lines. An artificial tangential velocity has been added to the Lagrangian markers to ensure that the markers are uniformly distributed at all times. The corresponding modified surfactant equation is solved in a way such that the total surfactant mass is conserved. Numerical experiments including convergence analysis are carefully conducted. The effect of the surfactant on the motion of hydrophilic and hydrophobic drops are investigated in detail.