We propose a new surfactant transport model on the interface based on the phase-field method. The new model has two features: (a) preventing surfactants on the interface from leaking out of the interface due to numerical diffusion even when the diffusion coefficient is extremely low, and (b) satisfying the conservation of surfactant mass. The concentration profile on the interface is matched to the surface delta function to prevent numerical diffusion, and the finite volume method is applied to the resulting model to satisfy the conservation of surfactant mass. The proposed model is incorporated in a weakly compressible scheme and applied in several numerical tests related to incompressible two-phase flows with surfactants. Numerical results show that the proposed model can be applied to various incompressible two-phase flow simulations with surfactant.