We investigate the energy levels of two qubits that are coupled via ■_1z ■ ■_2z Ising-type of coupling. We demonstrate that two flux qubits can be coupled to form a quantum mechanical four level system. We not only investigate how the energy bias εand tunneling amplitude t affect the energy levels,but also especially analyze the effect of the coupling factor j(both coupling strength and coupling direction)between two qubits. The results indicate that,for a two identical qubits system,not only the energy level of two antiferromagnetic states but also the transition frequency between them at Φ =(1/2)Φ₀ is controlled by the coupling factors.