In this study, the influences of silicon-based gas barrier films fabricated by using a facing target sputtering(FTS) system on the gas permeability for flexible displays have been investigated. Under these optimum conditions on the $SiO_x$ film with oxygen concentration($O_2/Ar+O_2$) of 3.3% and the $SiO_xN_y$ film with nitrogen concentration($N_2/Ar+O_2+N_2$) of 30% deposited by the FTS system, it was found that the films were grown about 4 times higher deposition rate than that of the conventional sputtering system and showed high transmittance about 85% in the visible light range. Particularly, the polyethylene naphthalate(PEN) substrates with the $SiO_x$ and/or $SiO_xN_y$ films showed the enhanced properties of decreased water vapor transmission rate (WVTR) over $10^{-1};g/m^2{cdot}day$ compared with the PEN substrate without any gas barrier films, which was due to high packing density in the Si-based films with high plasma density by FTS process and/or the denser chemical structure of Si-N bond in the $SiO_xN_y$ film.