Film boiling on a horizontal 2D plane has been investigated and simulated by a numerical method here. Using a finite difference front tracking method (a certain discretization method) ,energy and momentum equations are solved for both phases. Moreover, intertia, vescosity, and surface tension terms have been included in this simulation. The influence of size or length of the domain ,the temperature difference ( ) which alter the Jacob number, and the change of Grashof number (due to change of gravitational acceleration and surface tension coefficient) on the interface, heat transfer, and fluid flow have been simulated. The simulations are followed until some bubble rise and a steady state for the investigation of the Nusselt number is reached. Although the instantaneous Nusselt number changes, it reaches a statistically mean value .As the Jacob number increases and the Grashof number decreases, there may be no alternating bubble rise and a vapor jet (which acts as a vapor film interconnecting the hot wall vapor film to the upper layer of vapor located on the liquid free surface) may also form. Finally, different heat fluxes are also imposed on the hot wall as well as constant temperatures and the movement and growth of the interface, in addition to the temporal change of the Nussulet number, is be investigated for different heat fluxes. Keywords : Film boiling on flat surface, Front tracking method, heat transfer, heat flux