In this work, we demonstrate a dual-wavelength passively mode-locked erbium-doped fiber laser employing graphene nanoplatelet as saturable absorber. The dual-wavelength laser is generated in ~1530 nm and ~1550 nm wavelength regions by splitting the main signal into two separate laser oscillations via a red/blue wavelength division multiplexer. Both the unidirectional and bidirectional dual-wavelength oscillation scheme are investigated, and it is found that the latter is advantageous in providing narrower pulse widths of 890 fs and 980 fs for the respective wavelength region, on top of boosting the pulse energy to the maximum value of 139 pJ and 155 pJ, respectively. It is believed that the bidirectional dual-wavelength oscillation scheme can minimize the overlapping effect between the neighboring pulses that cause pulse distortion as well as signal attenuation compared with unidirectional dual-wavelength oscillation. This work expands the dynamics of cavity structure design for synchronized dual-wavelength mode-locked fiber laser generation.