The invention discloses a memristor-based bandwidth adjustable low-pass filter circuit and an operation method thereof. The circuit is composed of a first-order active low-pass filter circuit including a memristor and a programming circuit including a memristor. The threshold voltage characteristics of the memristor are utilized, the working modes of the memristor are divided into an analog working mode and a programming working mode, and the bandwidth of the filter circuit is changed by changing the resistance value of the memristor. The programming circuit is composed of the memristor, four NMOS tubes and four PMOS tubes. The first-order active filter circuit is composed of the memristor, a capacitor and an operational amplifier. The invention also discloses a memristor-based bandwidth adjustable high-pass filter circuit and an operation method thereof. The circuit has the advantages that the active filter circuit is low in input impedance and high in output impedance, and the programming circuit has the advantages of being small in volume occupation, high in degree of integration, low in power consumption and easy to operate so that the circuit is suitable for signal filtering processing.