Recently topological materials have attracted much attention due to their quantization transports as well as edge states. It will be excellent to realize the robust quantum anomalous Hall transports in graphene-based devices. Using density-functional theory and tight-binding method, we investigated the structural, magnetic and topological properties for the boron-doped graphene with Re-adsorption. A large band-gap of 32.5 meV is opened by the Rashba spin-orbital coupling, and the band-gap is robust against the shape deformation of ±[Formula: see text] along the zigzag direction. Giant magnetic anisotropy emerges in this adsorption system together with the Fermi level lying in the band gap. Both the magnetic anisotropy and the band gap can be tuned by a moderate electric field. Calculations reveal that the system exhibits the quantization transports with the Chern number [Formula: see text].