As a two-dimensional material with single-layer carbon atoms, the absorptivity of graphene is only about 2.3% in visible and near-infrared region, which restricts its applications in photoelectric detection, modulation and solar cells. A way to enhance the graphene absorption in this wavelength region is to combine graphene with grating nanostructure. The grating nanostructure can generate strong near-field localization by magnetic polaritons (MPs). However, the existing structures based on MPs are facing some problems, such as sensitivity to the polarization direction of the incoming wave and difficulty in processing the deep grating. Moreover, the modulation effect of the hybrid nanostructure based on MPs combining graphene with nano-grating has not been studied. In this work, a hybrid two-dimensional shallow grating nanostructure is proposed to modulate the absorptivity of graphene based on MPs. The finite element simulation is conducted to calculate the absorptive properties. The equivalent circuit model is used to predict the resonance conditions. The current and field distributions further confirm the excitation of magnetic resonance. The influences of structural parameters and the chemical potential on absorption property are studied. The results show that the magnetic polaritons derived from the hybrid two-dimensional shallow grating structure can obviously improve the absorption of graphene in the near-infrared region. Under the specific structure, the overall absorptivity of the structure is 85%, and the absorptivity of graphene in the structure is 55%, which is over 24 times higher than that of free-standing monolayer graphene. The absorption spectra of the hybrid grating nanostructure for different geometric parameters are calculated. The results show that the absorption peak presents an obvious blue-shift as the thickness of the dielectric layer, the grating period or the width of the silver nanoparticles decrease. Numerical simulation results show that by adjusting the chemical potential of graphene, the overall absorptivity of the structure can be tuned dynamically. The reflection modulation depths of hybrid two-dimensional nanostructure under different structural parameters are calculated. By controlling the chemical potential of graphene in a range from 0.1 eV to 1 eV, the reflection modulation depths of 54.8% (1040 nm), 50.3% (890 nm) and 46.8% (750 nm) are obtained, respectively. Compared with the existing structures based on MPs, the present structure is insensitive to the incidence and polarization direction of the incident electromagnetic wave due to the symmetry in two-dimensional directions. Considering the design of shallow silver grating, the structure is easier to implement in the process. The research results provide good theoretical reference for graphene-based photoelectric detection and modulation.