The bidirectional operation of a single-wall carbon nanotube-based passively mode-locked erbium-doped soliton fiber laser without isolator, is demonstrated with stable output pulse trains simultaneously from both directions of the laser cavity. The fiber laser consists of wavelength division multiplexer, erbium-doped fiber, optical coupler, carbon nanotube, single-mode fiber and polarization controller. By adjusting the pump power and polarization controller to analyse the output characteristics of experimental device under different pump powers , the center wavelengths of the two opposite pulses can be changed from 1 558~1 560 nm. The clockwise pulse width can be varied from 854~959 ps. The counter clockwise pulse width can be changed from 247~624 ps. Especially, the pulse split of the counterclockwise pulse trains has been observed.