We construct a sample of X-ray-bright optically faint active galactic nuclei by combining Subaru Hyper Suprime-Cam, XMM-Newton, and infrared source catalogs. Fifty-three X-ray sources satisfying i-band magnitude fainter than 23.5mag and X-ray counts with the EPIC-PN detector larger than 70 are selected from 9.1 deg^2^, and their spectral energy distributions (SEDs) and X-ray spectra are analyzed. Forty-four objects with an X-ray to i-band flux ratio FX/Fi>10 are classified as extreme X-ray-to-optical flux sources. Spectral energy distributions of 48 among 53 are represented by templates of type 2 AGNs or star-forming galaxies and show the optical signature of stellar emission from host galaxies in the source rest frame. Infrared/optical SEDs indicate a significant contribution of emission from dust to the infrared fluxes, and that the central AGN is dust obscured. The photometric redshifts determined from the SEDs are in the range of 0.6-2.5. The X-ray spectra are fitted by an absorbed power-law model, and the intrinsic absorption column densities are modest (best-fit logNH=20.5-23.5cm^-2^ in most cases). The absorption-corrected X-ray luminosities are in the range of 6x10^42^-2x10^45^erg/s. Twenty objects are classified as type 2 quasars based on X-ray luminosity and NH. The optical faintness is explained by a combination of redshifts (mostly z>1.0), strong dust extinction, and in part a large ratio of dust/gas.