A numerical method to simulate liquid-vapor phase change is presented. The method is based on the so-called single field formulation where one set of equations for conservation of mass, momentum and energy are written for the entire flow field. Interfacial source terms for surface tension, interphase mass transfer and latent heat are added as delta functions that are non-zero only at the phase boundary. The equations are discretized by a finite difference method on a regular grid and the phase boundary is explicitly tracked by a moving front. A comparison of numerical results to the exact solution of a one-dimensional test problem shows excellent agreement. The method is applied to film boiling, where vapor bubbles are generated from a thin film next to a hot wall. Although the film boiling simulations presented here are two-dimensional, the resulting heat transfer rate and wall temperatures are found to be in good agreement with experimental observations.