We present the single-epoch black hole mass ( M _ { BH } ) calibrations based on the rest-frame UV and optical measurements of Mg ii 2798Å and H \beta 4861Å lines and AGN continuum , using a sample of 52 moderate-luminosity AGNs at z \sim 0.4 and z \sim 0.6 with high-quality Keck spectra . We combine this sample with a large number of luminous AGNs from the Sloan Digital Sky Survey to increase the dynamic range for a better comparison of UV and optical velocity and luminosity measurements . With respect to the reference M _ { BH } based on the line dispersion of H \beta and continuum luminosity at 5100Å , we calibrate the UV and optical mass estimators , by determining the best-fit values of the coefficients in the mass equation . By investigating whether the UV estimators show systematic trend with Eddington ratio , FWHM of H \beta , the Fe ii strength , and the UV/optical slope , we find no significant bias except for the slope . By fitting the systematic difference of Mg ii-based and H \beta -based masses with the L _ { 3000 } /L _ { 5100 } ratio , we provide a correction term as a function of the spectral index as \Delta C = 0.24 ( 1+ \alpha _ { \lambda } ) + 0.17 , which can be added to the Mg ii-based mass estimators if the spectral slope can be well determined . The derived UV mass estimators typically show > \sim 0.2 dex intrinsic scatter with respect to H \beta -based M _ { BH } , suggesting that the UV-based mass has an additional uncertainty of \sim 0.2 dex , even if high quality rest-frame UV spectra are available .