Abstract: In this paper, based on the cubic polynomial relation between charge q and magnetic flux \varphi, a novel cubic flux-controlled memristor model is proposed and verified by MATLAB simulation. Applying the principle of "floating ground" two port equivalent circuit, the equivalent circuit of the cubic flux-controlled memristor and its low-pass and high-pass filters are designed and implemented, and the simulation is carried out on PSPICE. Finally, the actual circuits of the cubic flux-controlled memristor and its low-pass and high-pass filters are built and tested by oscilloscope. The experimental and simulation results show that the low-pass filter based on the novel flux-controlled memristor has a lower output gain than the resistor-based one, while high-pass filter based on the novel flux-controlled memristor is basically consistent with the output gain based on resistor.