The method of Gutzwiller in the problem of electron correlation in the Hubbard model is extended to the antiferromagnetic state. It is shown that the transition from the paramagnetic to the antiferromagnetic state occurs at a certain value of U (intraatomic Coulomb energy) for a fixed value of the electron concentration. In contrast to the result in the Hartree-Fock approximation, this value of U does not vanish even in the case when the magnetic zone boundary coincides with the Fermi surface. For extremely large values of U, the critical electron concentration is shown to approach to 1/2. Special care is taken in the case of the half-filled band, and our ground state energy is compared with that in the Hartree-Fock approximation. It is shown that for large value of U the Hartree-Fock energy is lower, but that for intermediate value of U our energy becomes lower for the special band structure.