A highly selective tunable filter with switchable bandpass (BP)-to- bandstop (BS) frequency response is designed. The frequency of the filter can be adjusted by loading a varactor diode on the end of microstrip resonator and branch; a PIN diode can be used to switch BP and BS characteristics. The filter is analyzed using the even- and odd-mode method, and constant absolute bandwidth (CABW) is achieved. Then, a source and load coupling is introduced so that there is a transmission zero (TZ) on each side of band, which can be almost keep in the same relative position throughout the frequency tuning range (FTR). Therefore, in the FTR, the filter achieves high selectivity and good out-of-band suppression characteristics. The FTR of the proposed filter is 5.58～5.89 GHz, the measured attenuation within the stopband is greater than 14 dB with CABW of (80±5) MHz under BS state; the FTR is 5.42-5.79 GHz, CABW is (120±5) MHz, the measured return loss and insertion loss within the passband are about 13 dB and 1.69-2.25 dB under BP state, respectively. Moreover, the fabricated tunable filter has a compact size of 0.28λ_g×0.62λ_g (λ_g is the wavelength of the center frequency during the FTR). The experimental and simulated results are in good agreement.