The selective laser-melting (SLM) process can be applied to the additive building of complex metal parts using melting metal powder with laser scanning. A metal mesh is a common type of metal screen consisting of parallel rows and intersecting columns. It is widely used in the agricultural, industrial, transportation, and machine protection sectors. This study investigated the fabrication of parts containing a mesh pattern from the SLM of AISI 304 stainless steel powder. The formation of a mesh pattern has a strong potential to increase the functionality and cost-effectiveness of the SLM process. To fabricate a single-layered thin mesh pattern, laser layering has been conducted on a copper base plate. The high thermal conductivity of copper allows heat to pass through it quickly, and prevents the adhesion of a thin laser-melted layer. The effects of the process conditions such as the laser scan speed and scanning path on the size and dimensional accuracy of the fabricated mesh patterns were characterized. As the analysis results indicate, a part with a mesh pattern was successfully obtained, and the application of the proposed method was shown to be feasible with a high degree of reliability.