Inducing local spin-polarization in pristine graphene is highly desirable and recent experiment shows that boron adatom chemical attachment to graphene exhibits local high spin state. Using hybrid exchange-correlation functional, we show that boron (B) monomer chemisorbed on the bridge site of graphene is energically favorable, and indeed induces a weak local spin-polarization ~0.56 μB. The localized magnetic moment can be attributed to the charge transfer from boron atom to graphene, resulting in local spin charge dominantly surrounding to the adsorbed B and neighboring carbon (C) atoms. We also surprisingly find that boron dimer can even much more stable upright anchor the same site of graphene, giving rise to sizable spin magnetic moment 2.00 μB. Although the apparent spin state remains mainly contributed by B p and C p orbitals as the case of boron monomer, the delicate and substantial charge transfer of the intra-dimer plays a fundamental role in producing such sizable local spin-polarization. We employed various van der Waals corrections to check and confirm the validity of appeared local spin-polarization. In terms of the almost identical simulated scanning tunneling microscope between boron monomer and dimer, we might tend to support the fact that boron dimer can also be chemisorbed on graphene with much larger and stable localized spin magnetic moment.