The origin of high-temperature superconductivity has been widely debated since its discovery. Here, a model based on the interaction between carrier and local potential is proposed to reveal the mechanism. In this model, the potential that is analogous to the lattice point is composed of localized charges, whose vibration mediates the coupling of mobile carriers. A Hamiltonian that describes the vibration, coupling and various interactions among the ordered potentials and carriers is established. By analyzing the Hamiltonian, it is found that the vibration of local potential and the interactions, which are dependent on the carrier density, control the transition temperature. We show that the transition temperature is high if the local potential is composed of electrons and the mobile carrier is hole because of the strong coupling between them. By replacing the local potential with lattice point, the proposed model is equivalent to that in the BCS theory. Therefore, our model may provide a general theoretical description on the superconductivity.