This study proposes a high-temperature superconducting (HTS) bandpass filter with a continuously tunable bandwidth and center frequency. The proposed filter combines several gallium arsenide varactors and a dual-mode resonator (DMR). The even and odd modes of the DMR can be tuned simultaneously using a single bias voltage. The capacitive value of varactors in the circuit is tuned continuously under continuous voltage and frequency tunability. External couplings and the interstage can be realized using an interdigital coupling structure; a fixed capacitor is added to the feeder to improve its coupling strength. A low-insertion loss within the band is obtained using HTS technology. Additionally, the proposed filter is etched on a 0.5 mm-thick MgO substrate and combined with YBCO thin films for demonstration. For the as-fabricated device, the tuning frequency range of 1.22~1.34 GHz was 9.4%; the 3-dB fractional bandwidth was 12.95~17.39%, and the insertion loss was 2.28~3.59 dB. The simulation and experimental measurement results were highly consistent.