The structural electronic and optical properties of intermetallic compound MgRh were investigated by using the ab-initio technique from CASTEP code. In this study we have carried out the pseudopotential plane-wave (PP-PW) method based on the density functional theory (DFT), within the generalized gradient approximation (GGA). Our calculated structural parameters and corresponding graphical values fit with other previous available experimental data and other theoretical observations. The calculated electronic band structure reveals metallic conductivity and the major contribution comes from Rh-d states. Comparison between our investigated properties and experimental data shows good agreement. The optical functions (dielectric functions, refractive index, absorption spectrum, conductivity, energy loss spectrum and reflectivity) have been calculated and discussed. This is the first quantitative prediction of the electronic and optical properties of intermetallic compound MgRh alloy, since it has not been reported yet. The calculated optical functions reveal that the reflectivity is high in the ultraviolet region up to 73 eV for MgRh, showing this to be promising coating materials.