In this paper, we propose a graphene-dielectric metasurface to enhance the light-matter interactions in graphene. The dielectric metasurface consists of periodically arranged silicon split rings placed on the silica substrate, which supports a symmetry-protected bound state in the continuum (BIC). When perturbation is introduced into the system to break symmetry, the BIC will transform into the quasi-BIC with high quality (Q)-factor. As the graphene layer is integrated with the dielectric metasurface, the absorption of graphene can be enhanced by the quasi-BIC resonance and a bandwidth-tunable absorber can be achieved by optimizing the Fermi energy of graphene and the asymmetry parameter of the metasurface to satisfy the critical coupling condition. By varying the Fermi energy of graphene, the quasi-BIC resonances can be effectively modulated and the max transmission intensity difference is up to 81% and a smaller asymmetry parameter will lead to better modulation performance. Our results may provide theoretical support for the design of absorber and modulator based on the quasi-BIC.