Selective laser melting is a frequently used, powder bed fusion additive manufacturing technology for producing metallic parts. However, appropriate surface quality cannot be achieved, so post-processing is often necessary. Subsequent machining of surfaces serves multiple objectives such as improvement of dimensional accuracy, changing surface roughness and modification of the residual stress state for higher surface hardness. Beyond its several advantageous properties, Ti6Al4V material has, as its weaknesses, low tribological behavior and wear resistance. Sliding friction burnishing is a conventional chipless and coolant-free environmentally conscious technology for surface modification that is appropriate for simultaneously decreasing surface roughness and increasing surface hardness. Until now, there has been a research gap regarding the diamond burnishing of selective laser melted Ti6Al4V parts. In this study, we investigated how the surface roughness of selective laser melted parts can be modified via sliding friction burnishing. 2D and 3D characteristics of surface roughness were measured by a chromatic roughness measuring device. Indices of surface roughness improvement were defined and studied as a function of selective laser melting parameters. Optimal manufacturing parameters of laser power—P = 280 W and scanning speed u = 1200 mm/s—for effective surface improvement via burnishing are proposed.