The mechanical properties of selective laser melting (SLM) components are fundamentally dependent on their microstructure. Accordingly, the present study proposes an integrated simulation framework consisting of a three-dimensional (3D) finite element model and a cellular automaton model for predicting the epitaxial grain growth mode in the single-track SLM processing of IN718. The laser beam scattering effect, melt surface evolution, powder volume shrinkage, bulk heterogeneous nucleation, epitaxial growth, and initial microstructure of the substrate are considered. The simulation results show that during single-track SLM processing, coarse epitaxial grains are formed at the melt–substrate interface, while fine grains grow at the melt–powder interface with a density determined by the intensity of the heat input. During the solidification stage, the epitaxial grains and bulk nucleated grains grow toward the top surface of the melt pool along the temperature gradient vectors. The rate of the epitaxial grain growth varies as a function of the orientation and size of the partially melted grains at the melt–substrate boundary, the melt pool size, and the temperature gradient. This is observed that by increasing heat input from 250 J/m to 500 J/m, the average grain size increases by ~20%. In addition, the average grain size reduces by 17% when the initial substrate grain size decreases by 50%. In general, the results show that the microstructure of the processed IN718 alloy can be controlled by adjusting the heat input, preheating conditions, and initial substrate grain size.