The invention provides a narrow bandwidth tunable filter and a preparation method. The narrow bandwidth tunable filter comprises a substrate and a transmission cavity and a DC offset line which are arranged on the surface of the substrate. The transmission cavity comprises an SQUID chain. The transmission cavity is used for filtering frequency bands which are different from its resonant frequency of input signals and the frequency bands which are the same with the resonant frequency of output signals. The DC offset line is used for providing a magnetic field for the SQUID chain. The resonant frequency of the transmission cavity is determined by the total capacitance and the total inductance of the SQUID chain. The total inductance of the SQUID chain changes along with the change of the size of the magnetic field, and the size of the magnetic field changes along with the change of the size of the current in the DC offset line so that the work frequency of the transmission cavity can be adjusted by adjusting the size of the current of the DC offset line, then the work bandwidth of the filter can be adjusted and processing of the substantially variable frequency signals can be realized; besides, the transmission cavity includes the SQUID chain, and the SQUID chain is a superconducting quantum interferometer structure so that narrow bandwidth filtering of the filter can be realized.