The correlation of screw-instability in black hole magnetosphere withpairs of high-frequency quasi-periodic oscillations (HFQPOs) isdiscussed in the coexistence of the Blandford–Znajek (BZ) and magneticcoupling (MC) processes. It turns out that screw-instability can resultin HFQPOs. Such an HFQPO can be regarded as the transient process in anequivalent 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 screw-instabilitycan occur both in the BZ region and in the MC region, and the pairs ofHFQPOs can be generated. Calculations show that such pairs of HFQPOs arelikely to show frequencies in a 3:2 ratio. The frequencies of pairs ofHFQPOs in our model scale inversely with the mass of central black hole,which is consistent with the observations.