This paper presents a high-selectivity dual-band bandpass filter with independently-tunable passband frequencies. A tap-coupled structure is utilized to feed the two resonators at lower passband and a coupling structure is used to feed the two resonators at the upper passband. Two pairs of varactor-loaded resonators operating within two different frequency ranges, allow the independent passband frequency tuning. Using this configuration, it is convenient to tune the center frequency of each passband, while the responses of the other passband remain unaltered. Source-load coupling is realized to generate transmission zeros, resulting in high skirt-selectivity. The transmission zeros move synchronously with the passbands, ensuring sharp roll-off rate for all tuning states. To verify the proposed idea, a demonstration microstrip tunable bandpass filter is implemented. The simulated and measured results are presented.