We combine photometric data from GALEX GR6+7 All-Sky Imaging Survey and Gaia Early Data Release 3 with stellar parameters from the SAGA and PASTEL catalogs to construct high-quality training samples for dwarfs (0.4<BP-RP<1.6) and giants (0.6<BP-RP<1.6). We apply careful reddening corrections using empirical temperature- and extinction-dependent extinction coefficients. Using the two samples, we establish a relationship between stellar loci (near-ultraviolet (NUV)-BP versus BP-RP colors), metallicity, and MG. For a given BP-RP color, a 1dex change in [Fe/H] corresponds to an approximately 1mag change in NUV-BP color for solar-type stars. These relationships are employed to estimate metallicities based on NUV-BP, BP-RP, and MG. Thanks to the strong metallicity dependence in the GALEX NUV band, our models enable a typical photometric-metallicity precision of approximately {sigma}[Fe/H]=0.11dex for dwarfs and {sigma}[Fe/H]=0.17dex for giants, with an effective metallicity range extending down to [Fe/H]=-3.0 for dwarfs and [Fe/H]=-4.0 for giants. We also find that the NUV-band-based photometric-metallicity estimate is not as strongly affected by carbon enhancement as previous photometric techniques. With the GALEX and Gaia data, we have estimated metallicities for about 5 million stars across almost the entire sky, including approximately 4.5 million dwarfs and 0.5 million giants. This work demonstrates the potential of the NUV band for estimating photometric metallicities, and sets the groundwork for utilizing the NUV data from space telescopes such as the upcoming Chinese Space Station Telescope.