Based on the Bragg grating/metallic film asymmetric resonant cavity, a multi-layer film structure that enhances the ultraviolet absorption of graphene is designed. The transfer matrix method is used to simulate and calculate the correlation between the film structure parameters and the absorption spectra of graphene. As a result, the optimal structure parameters are obtained. The calculation results show that the resonance effect of the asymmetric resonant cavity strongly promotes the interaction between incident light and graphene. After optimization, the ultraviolet absorption of graphene at 275 nm is up to 0.9534 and the full width at half maximum is only 2.0 nm. Further research indicates that the central wavelength of the Bragg grating and the incident angle of light can regulate the wavelength and size of the graphene absorption peak. Increasing the number of graphene layers is able to enhance the ultraviolet absorption of graphene and expand absorption spectra. The proposed structure can also promote the ultraviolet absorption of other wide-band-gap two-dimensional materials.