Approach-to-equilibrium molecular dynamics (AEMD) is a widely used molecular dynamics (MD) method to extract thermal transport properties in different material systems. Despite the success in many applications, the thermal transport mechanism in AEMD is not well understood. Although AEMD can simulate larger domain than other MD variants, it still suffers from simulation domain size effect. In addition, the size effect is quite different from that of the nonequilibrium molecular dynamics (NEMD) simulations. In this paper, we reveal the phonon transport mechanism in AEMD by comparing the size-dependent thermal conductivity values of AEMD and phonon Boltzmann transport equation. We show that the simulation size of AEMD should be defined as half of the size in the conventional AEMD simulations with periodic boundary conditions. Also, the size effect in AEMD originates from ballistic phonon transport. Different from NEMD, some phonons with long mean-free paths do not contribute to the thermal conductivity, resulting in a smaller thermal conductivity than NEMD with the same size. Based on the phonon transport mechanism in AEMD, we suggest an extrapolation method for AEMD to obtain bulk thermal conductivity.