The variational approach initiated by Gutzwiller is extended to include antiferromagnetism. A simplified assumption corresponding to that adopted by him is used in order to evaluate the ground state energy of the Hubbard model and to draw the phase diagram similar to those constructed by Penn on the basis of the Hartree-Fock approximation. It is found that the antiferromagnetic state in the phase diagram is restricted to a narrow region bounded by threshold values for both the coupling constant and electron density. For sufficiently large intraatomic repulsion paramagnetic state becomes more stable than antiferromagnetic state except for the case of one electron per site. The phase transition between paramagnetic and antiferromagnetic states is of first order and the coexistence of these two states with different density occurs.