We investigated Raman spectra of single-layer and multilayer graphene under ultraviolet laser excitation at the wavelength λ=325 nm. It was found that while graphene's G peak remains pronounced in UV Raman spectra, the 2D -band intensity undergoes severe quenching. The evolution of the ratio of the intensities of the G and 2D peaks, I (G) /I (2D), as the number of graphene layers n changes from n=1 to n=5, is different in UV Raman spectra from that in conventional visible Raman spectra excited at the 488 and 633 nm wavelengths. The 2D band under UV excitation shifts to larger wave numbers and is found near 2825 cm-1. The observed UV Raman features of graphene were explained by invoking the resonant scattering model. The obtained results contribute to the Raman nanometrology of graphene by providing an additional metric for determining the number of graphene layers and assessing its quality.