Graphene is an ideal ultrathin material for various optoelectronic devices, but poor light–graphene interaction limits its further applications particularly in the visible (Vis) to near-infrared (NIR) region. Despite tremendous efforts to improve light absorption in graphene, achieving highly efficient light absorption of monolayer graphene within a comparatively simple architecture is still urgently needed. Here, we demonstrate the interesting attribute of bound state in the continuum (BIC) for highly efficient light absorption of graphene by using a simple Si-based photonic crystal slab (PCS) with a slit. Near-perfect absorption of monolayer graphene can be realized due to high confinement of light and near-field enhancement in the Si-based PCS, where BIC turns into quasi-BIC due to the symmetry-breaking of the structure. Theoretical analysis based on the coupled mode theory (CMT) is proposed to evaluate the absorption performances of monolayer graphene integrated with the symmetry-broken PCS, which indicates that high absorption of graphene is feasible at critical coupling based on the destructive interference of transmission light. Moreover, the absorption spectra of the monolayer graphene are stable to the variations of the structural parameters, and the angular tolerances of classical incidence can be effectively improved via full conical incidence. By using the full conical incidence, the angular bandwidths for the peak absorptivity and for the central wavelength of graphene absorption can be enhanced more than five times and 2.92 times, respectively. When the Si-based PCS with graphene is used in refractive index sensors, excellent sensing performances with sensitivity of 604 nm/RIU and figure of merit (FoM) of 151 can be achieved.