In this paper, we propose novel plasmonic hydrogen sensors based on palladium coated narrow-groove plasmonic nanogratings for sensing of hydrogen gas at visible and near-infrared wavelengths. These narrow-groove plasmonic nanogratings allow the incident light to be coupled directly into plasmonic waveguide modes thereby alleviating the need for bulky coupling methods to be employed. We carried out numerical simulations of the palladium coated narrow-groove plasmonic nanogratings using rigorous coupled wave analysis (RCWA). When palladium is exposed to varying concentrations of hydrogen gas, palladium undergoes phase transition to palladium hydride (PdHx), such that there are different atomic ratios ‘x’ (H/Pd) of hydrogen present in the palladium hydride (PdHx) depending on the concentration of the hydrogen gas. RCWA simulations were performed to obtain the reflectance spectral response of the Pd coated nanogratings in both the absence and presence of hydrogen, for various atomic ratios ‘x’ (x ∼ 0.125 to 0.65) in palladium hydride (PdHx). The results of the RCWA simulations showed that as the dielectric permittivity of the palladium (Pd) thin film layers in between the adjacent walls of the plasmonic nanogratings changes upon exposure to hydrogen, significant shifts in the plasmon resonance wavelength (maximum Δλ being ∼80 nm for an increase in the value of the atomic ratio ‘x’ from 0 to 0.65) as well as changes in the differential reflection spectra are observed. The structural parameters of these Pd coated narrow groove nanogratings—such as the nanograting height, gap between the nanograting walls, thickness of the palladium layer, periodicity of the nanogratings—were varied to maximize the shift in the plasmon resonance wavelength as well as the differential reflectance when these nanostructures are exposed to different concentrations of hydrogen (i.e. for different atomic ratios ‘x’ in PdHx).