We propose the mechanism for the magnetic field induced AFM state in a two-dimensional Hubbard model in the vicinity of the antiferromagnetic (AFM) quantum critical point (QCP),using the fluctuation-exchange (FLEX) approximation by taking the Zeeman energy due to magnetic field B into account. In the vicinity of the QCP, we find that the AFM correlation perpendicular to B is enhanced, whereas that parallel to B is reduced. This fact means that the finite magnetic field enhances TN, with the AFM order perpendicular to B. The increment of TN can be understood in terms of the reduction of both the quantum and the thermal fluctuations due to the magnetic field, which is brought by the self-energy effect within the FLEX approximation. The present study naturally explains the increment of TN in CeRhIn5 under the magnetic field found recently.