We demonstrated a continuously wavelength-tunable bidirectional passively Q-switched fiber laser based on a single-walled carbon nanotube saturable absorber and a bandpass filter (BPF). By tuning the commercial BPF, the Q-switched pulse can be obtained in the same cavity at the same pump power in clockwise (CW) and counterclockwise (CCW) directions. The central wavelength can be continuously tuned from 1520.88 to 1568.56 nm in the CW direction, and from 1520.96 to 1568.64 nm in the CCW direction. A wide tuning range of 48 nm is achieved for two directions in the passively Q-switched fiber laser.During the tuning process of the fiber laser, the output pulses with the same central lasing wavelength can be obtained in both oscillation directions owing to the BPF. By increasing the pump power from 130 to 350 mW, the cavity delivers a Q-switched pulse with the central wavelength of 1560 nm whose repetition rate changes from 9.64 to 59.18 kHz for the CW direction. In the CCW direction, the repetition rate of the Q-switched pulse changes from 10.26 to 61.03 kHz. To the best of our knowledge, it is the first time that continuous wavelength-tunable passively Q-switched pulses have been achieved in a bidirectional erbium-doped fiber laser.