We demonstrate the modulation of laser bandwidth by utilizing an ultranarrow tunable bandpass filter (UNTBF) in a passively Q-switched erbium-doped fiber laser. The passive Q-switch mechanism is enabled by using carbon nanotubes as saturable absorber at a Q-switched threshold of 35.5 mW. Based on spectral filtering effect introduced by the UNTBF, the 3 dB laser bandwidth can be tuned from 0.016 nm to 0.478 nm at a fixed pump power of 75.9 mW. The corresponding pulse behavior for each different bandwidth is characterized, and the results reveals that the pulse width can be as well tuned from 7.8 to 2.6 μs against the laser bandwidth, which agrees with the rule of time-bandwidth product. Correspondingly, the pulse repetition rate and the pulse energy vary from 16.23 kHz to 26.16 kHz and from 0.67 to 1.03 μJ respectively across the laser bandwidth. Further investigation of the pulse performance is performed against the pump power increment up to 107.2 mW. To the best of our knowledge, this is the first demonstration of spectrum bandwidth modulation in a passively Q-switched fiber laser, which can be useful for fully exploiting the possibilities of Q-switched pulse applications.