To investigate the optical properties of plasmonic nanoparticles and the formation of localized surface plasmon, an optical spectroscopy setup using light-emitting diodes (LEDs) as light sources is designed. The proposed system can be used to measure extinction spectra, scattering spectra, size and concentration of nanoparticles in a solution, fluorescence enhancement by plasmonic nanoparticles, and the effect of nanoparticles size on their optical properties. As an experimental test, we consider determination of silver nanoparticles size in aqueous solvent and compare it with data obtained from the dynamic light scattering (DLS) method.