The transformation method in reference 1 is extended to treat the lattice composed of different spin atoms (Sa=l, Sb= l/2), the ground state's spin structure, energy and phase boundary of the simply cubic lattice with ihird nearest neighbors, next nearest neighbors and nearest neighbors antiferromagnetic interaction haye been calculated in an arbitrary magnetic field. We conclude that the lattice possesses two antiferromagnetic spin structures and four subferromagnetic spin structures from the phase diagrams.