Additive manufacturing (AM) of metal has been experiencing rapid growth in recent years by employing a variety of techniques. Among them, selective laser melting (SLM) of metal exhibits advantages in terms of its capabilities to build complex geometries, good surface finish, and high dimensional accuracy. Due to these benefits, SLM has demonstrated the ability to create metallic parts that can be applied in aerospace, automotive, and medical industries. However, most parts are geometrically complex with curved surface features, which would be difficult to be fabricated through traditional manufacturing methods. In order to increase the adoption and effectiveness of SLM for metal parts fabrication, the as-built surface finish and dimensional accuracy of the parts with curved surface features should be well understood. Great attempts have been made to investigate the surface texture of SLM as-built parts with various surface types. Most investigations characterize the surface texture of SLM-fabricated specimens with planar surface features. However, little is known about the surface finish and dimensional accuracy of SLM-fabricated metal parts with curved surfaces. Directly applying knowledge derived from planar surfaces to curved ones can be misleading. In this work, stainless steel 316L parts with curved surface features were built using SLM to examine the surface finish and dimensional accuracy. The results showed that 11 surface texture variables were significant at five different curvatures and the three most significant roughness variables were Sk, Spc, and Vmc. It was found that curvatures C1 and C5 significantly differed from the other curvatures (C2, C3, and C4) in all the 11 surface texture variables. In addition, the thickness of the as-built curved surface part at varied curvature locations would be almost constant.