Understanding the grain structure in metal additive manufacturing (MAM) builds is important to improve the properties of MAM builds and the controllability of MAM processes. The formation of the columnar and/or equiaxed grains in MAM are caused by an interplay of nucleation and growth mechanisms, which is numerically investigated in this work. A meso-scale Cellular Automata model combined with a macro-scale thermal model is used to predict the three-dimensional grain structure in the direct laser deposition process of stainless steel 304, with the investigation focused on the effects of the nucleation mechanisms (both the epitaxial nucleation at the fusion line and the bulk nucleation in the molten metal) on the grain structure. Our results show that the bulk nucleation condition can significantly change the grain structure (from columnar to equiaxed), and typical grain structures in MAM can be successfully reproduced using different bulk nucleation conditions.