We present an all-fiber bidirectional passively mode-locked soliton laser with a graphene-based saturable absorber for the first time to the best of our knowledge. Our design includes a four-port circulator to introduce different sections of cavity for the two counter-propagating pulses, so they have distinct output characteristics. Simultaneous bidirectional operation is achieved by appropriately adjusting the net cavity birefringence and loss. In the clockwise direction, the laser emits ~750 fs pulses at 1561.6 nm, with a repetition rate of 7.68 MHz. In the counter clockwise direction, the central wavelength, pulse width, and repetition rate are 1561.0 nm, ~850 fs, and 6.90 MHz, respectively.