The correlation of screw-instability in black hole magnetosphere with pairs of high-frequency quasi-periodic oscillations (HFQPOs) is discussed in the coexistence of the Blandford-Znajek (BZ) and magnetic coupling (MC)processes. It tus out that screw-instability can result in HFQPOs. Such an HFQPO can be regarded as the transient process in an equivalent circuit with resistor and inductor in series (R-L circuit), and its period can be estimated by the relaxation time of this process. When the BZ process and the MC process coexist, the screwinstability can occur both in the BZ region and in the MC region, and the pairs of HFQPOs can be generated.Calculations show that such pairs of HFQPOs are likely to show frequencies in a 3:2 ratio. The frequencies of pairs of HFQPOs in our model scale inversely with the mass of central black hole, which is consistent with the observations.