The grain structure and texture of metal parts fabricated by selective laser melting (SLM) are of interest for their effect on the properties. The study of the SLM single track can reduce the variables to be concerned and, hence, facilitate the understanding of the development of grain and texture in the SLM process. In this work, the austenitic stainless 316L single tracks are fabricated at different scanning speeds, and they are characterized by electron backscattered diffraction (EBSD) from transverse, serial transverse, and longitudinal cross-sections. It is validated that curved grain is common in the SLM single track. The effects of the varied thermal gradient and the shape of the melt pool on competitive growth of grain are analyzed. All the three equivalent < 001 > orientations of the columnar grain are considered, which leads us to put forward a crystallographic feature of a favorable grain during the competitive growth in SLM. Such a crystallographic feature is validated by the texture of the SLM single track, especially the < 001 > // scanning direction (SD) texture.