Powder-bed fusion additive manufacturing of Ti-6Al-4 V has been of tremendous interest in both academia and industry. As the two ubiquitous microstructural features, columnar grain and microstructural banding in selective electron beam melting of Ti-6Al-4 V are systematically studied by experimental and simulation methods. Three basic build geometries (i.e. V-, I- and A-shaped parts) are employed to study the columnar grain growth behavior. We find that columnar prior β-Ti grains grow epitaxially and competitively by following the classic competitive grain growth model in additive manufacturing of Ti-6Al-4 V. It results in increasingly stronger crystallographic texture with the rising build height. We also observe the consistently occurring microstructural banding (∼100 µm in period) normal to build direction due to the overlapped heat affected zones that are formed in the layerwise thermal cyclic process. In addition, a large quantity of sub-columnar grains exist within the microstructure for selective electron beam melted Ti-6Al-4 V. It is demonstrated that the periodic microstructural banding determines the appearance of sub-columnar grains which may affect the competition behavior for the growth of columnar grains.