We report a switchable dual-wavelength soliton fiber laser based on graphene ternary composite, that is, graphene/SnO2/PANI film. The graphene composite is synthesized by the liquid-phase ultrasonic method, the composite is transferred into the laser cavity by the polymer-film method. The as-prepared graphene device not only can act as an excellent saturable absorber for mode-locking, but also induces a highly third-order nonlinear optical effect to form a filter for dual-wavelength pulse generation in the laser. By exploiting the dual-function of this device, the switchable dual-wavelength soliton operation of the fiber laser is stably initiated with a minimum pulse width of 1.25 ps, a fundamental repetition rate of 2.13 MHz, a pulse energy of 1.51 nJ and peak power of 1.2 kW.