We propose and demonstrate a dual-wavelength single-longitudinal-mode (SLM) fiber laser with switchable wavelength spacing based on a graphene saturable absorber (GSA) and a WaveShaper. By virtue of the excellent saturable absorption ability of graphene, the linewidths of the lasing wavelengths can be effectively reduced and eventually SLM operation can be obtained. The linewidths of both wavelengths are measured to be narrower than 7.3 kHz. The obtained results suggest that the graphene would be a good candidate nonlinear optical material for applications in related photonic fields, such as SLM oscillation generation for microwave generation and optical sensing.