Abstract: The equidistant multi-gap acceleration structure is an asynchronous acceleration structure, when the velocity of the particle in the accelerated structure changes significantly, the phase of the particles at each gap is different. Current theories based on thin lens approximation do not take into account the variation in the velocity of the particles in the accelerated structure. This is reasonable in cases where the energy gain in a single cavity is small relative to the particle energy or where the acceleration gradient is small. This treatment is no longer sufficient when there is a significant change in the velocity of the particle in the structure. In this paper, the longitudinal motion dynamics of the beam in this equidistant multi-gap acceleration structure are modeled. By numerical simulations the phase space trajectories are obtained. The phase space trajectories are used to analyze the particles motion in the structure. The energy variations of particles with different initial energies are calculated when the electrical field gradients and gap numbers are different. Results show that compared with the properties of the beam motion predicted by the thin lens approximation theory, phase space trajectories are different, and its effects on energy gain as functions of acceleration gradient, the input energy, the cell numbers and so on are studied.