Display omitted •The CoCrFeMnNi high-entropy alloy exhibits excellent printability.•Rapid cooling leads to epitaxial growth of fine cells within the melt-pools.•Repeated metal deposition induces grain selection via competitive grain growth.•Scanning strategy and grain selection govern microstructure evolution. The CoCrFeMnNi high-entropy alloy is a promising candidate for metal additive manufacturing. In this study, single-layer and multi-layer builds were produced by laser powder bed fusion to study microstructure formation in rapid cooling and its evolution during repeated metal deposition. CoCrFeMnNi showed good printability with high consolidation and uniform high hardness. It is shown that microstructure in the printed alloy is governed by epitaxial growth and competitive grain growth. As a consequence, a bi-directional scanning pattern without rotation in subsequent layers generates a dominant alternating sequence of two crystal orientations.