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Abstract Additive manufacturing (AM) processes produce unique microstructures compared with other manufacturing processes because of the large thermal gradient, high solidification rate and other local temperature variations caused by the repeated heating and melting. However, the effect of these thermal profiles on the microstructure is not thoroughly understood. In this work, a 3D cellular automaton method is coupled to a finite volume method to predict the grain structure of an alloy, e.g. Inconel 718, fabricated by AM. The heat convection due to thermocapillary flow inside the melt pool is resolved by the finite volume method for a real and accurate temperature field, while an enriched grain nucleation scheme is implemented to capture epitaxial grain growth following the mechanism identified from experiments. Simulated microstructure results are shown to be in qualitative agreement with experimental result and the effects of the process parameters on both thermal characteristics and the grain structure are identified. The 3D cellular automaton finite volume method results establish our approach as a powerful technique to model grain evolution for AM and to address the process-structure-property relationship. Graphical Abstract Unlabelled Image Highlights • A 3D cellular automata finite volume method for additive manufacturing is presented, including an enriched nucleation model • The grain structure in the Directed Energy Deposition of IN718 alloy is simulated by the proposed method • The effects of the processing parameters on the resulting grain structure of IN718 alloy are elaborated via the simulation • Sandwich- and zig-zag patterns of grain structure observed in experiments are captured and explained by the proposed model [ABSTRACT FROM AUTHOR]