In this work, a finite element/level set method is developed to simulate deposition of molten polymer bead onto a substrate and its cooling down. This method will be used for the simulation of the Fused Filament Fabrication (FFF) additive manufacturing process. Compared to previous works that use a multiphase flow of polymer and air, in this study the polymer flow is treated as a single-phase flow with a free surface. This method reduces the computation time without loss of accuracy as polymer behavior significantly dominates air behavior. The equations governing the fluid motion are solved on a finite element mesh, whereas the free surface is captured based on the level set method on another fixed mesh. Since the free surface is captured “implicitly” by the zero level of the level set function, coalescence between filaments are well defined and naturally performed. This model provides detailed information on the cooling process and the bonding formation during the molten polymer deposition process. The effects of control parameters (nozzle velocity, flow rate and temperature…) on the final deformed shapes of the printed parts are investigated. For the first time, the numerical results from 2D simulations are compared to optical micrographs of the longitudinal-section of the printed samples, which shows good agreement between numerical and experimental results.