Pseudopotential Lattice Boltzmann (LB) model is an effective mesoscopic method for liquid-vapor phase change simulations. In LB methods, calculations are often carried out in lattice units. Thus, a correct mapping from the lattice unit system to the physical unit system is crucial for accurate simulations of practical problems. The unit conversion for liquid-vapor phase change problems is more complicated than single-phase problems, because an equation of state (EOS) for a non-ideal fluid is introduced in the pseudopotential two-phase model. In the present work, a novel unit conversion method for the pseudopotential LB model is proposed. The basic strategy is to obtain the conversion relations of fundamental units by mapping the surface tension and EOS parameters related to fluid properties, and thus the unit conversion relations of other quantities are deduced. Numerical simulations of benchmark problems including the film evaporation and the bubble heterogeneous nucleation from a V-shaped cavity are carried out, and the simulation results are converted to the physical unit system by the proposed method. The numerical results demonstrate that the proposed method is able to recover the physical-unit latent heat of the fluid in the film evaporation problem. In the bubble nucleation from a V-shaped cavity problem, the conventional unit conversion method cannot derive the correct superheat temperature in physical unit, while the proposed method based on fundamental units recovers the critical superheat temperature which is consistent with the analytical result.