One-dimensional plasmonic nanogratings (1D-PNGs) with high aspect ratios and narrow grooves promise enhanced coupling for hybrid graphene systems with the localized surface plasmon of the metallic grating and graphene surface plasmons. However, both the fabrication of the 1D-PNG and the application of graphene to it are difficult. We developed 1D-PNGs with a high aspect ratio of 15 and narrow grooves of 100 nm in width using the tapered mold method and a dry graphene-transfer procedure. Raman spectroscopy measurements showed that monolayer graphene was successfully transferred onto the 1D-PNGs, and the graphene was strongly doped with Au in the 1D-PNGs. Graphene on narrow grooves (free-standing graphene) demonstrated an almost identical p-doping level to graphene on Au because the narrow groove width allowed sufficient doping by Au for graphene on grooves. Reflectance measurements showed that the 1D-PNGs exhibited polarization- and wavelength-selective absorption at infrared (IR) wavelengths, and the effect of graphene blue-shifted the absorption peak wavelength induced by the surface plasmon resonance of 1D-PNGs. Numerical calculations agree well with these experimental results and indicate that the electric field strongly localizes on graphene in the grooves. Moreover, the doping level tunes the absorption wavelength owing to the coupling with graphene plasmons and the surface plasmon resonance of 1D-PNGs. This could provide electrical tunability to the graphene plasmons. Our fabrication procedure produced hybrid graphene-1D-PNGs with high aspect ratios and narrow groove systems for IR wavelengths. This system can contribute to developing high-performance electrically tunable graphene-based IR photodetectors, tunable IR emitters/absorbers, and biological sensors.