This paper investigates the relationship between the speed of a quantum not gate and the asymmetry of the potential in an interactive system formed by a two-level RF-SQUID qubit and a classical microwave pulse.The RF-SQUID is characterized by an asymmetric double well potential which gives rise to diagonal matrix elements that describe the interaction of the SQUID with the microwave pulse.And the diagonal matrix elements account for the interaction of the microwave pulse with the SQUID.The results indicate that,when the angular frequency of the microwave field is chosen as near resonate with the transition |0>(→) |1>,i.e.ω1-ω0 ≈ωm,(1) the gate speed is decided by three factors,the Rabi frequency,the difference of the diagonal matrix elements between the two levels,and the angular frequency of the applied microwave pulse Wm;(2) the gate speed descends when the asymmetry of the potential is considered.