The modified Kadanoff variational method has been used to study a simple cubic Ising model with the nearest-neighbor two-spin interactions of strength J2 and the four-spin interactions of strength J4. The free energy f. spontaneous magnetization M, magnetic susceptibility x, internal energy U, and the specific heat Ch are calculated and plotted. The results indicate that for 0≤J4/J2≤4, the phase transitions are second-order.