In this paper, the Edge-Based Interface Tracking (EBIT) method is extended to simulate multiphase flows with phase change. As a novel Front-Tracking method, the EBIT method binds interfacial markers to the Eulerian grid to achieve automatic parallelization. To include phase change effects, the energy equation for each phase is solved, with the temperature boundary condition at the interface sharply imposed. When using collocated grids, the cell-centered velocity is approximately projected. This will lead to unphysical oscillations in the presence of phase change, as the velocity will be discontinuous across the interface. It is demonstrated that this issue can be addressed by using the ghost fluid method, in which the ghost velocity is set according to the jump condition, thereby removing the discontinuity. A series of benchmark tests are performed to validate the present method. It is shown that the numerical results agree very well with the theoretical solutions and the experimental results.