The stochastic resonance phenomenon for a fractional-order oscillator with multiplicative signal and random characteristic frequencies is studied. Under the condition of low driving frequency, the long-term analytical expression for the system output signal of the oscillator is derived by using the characteristics of the fractional-order operator. The results show that the resonance phenomenon of system output signal is observed, due to the interaction of multiplicative signal, noise and fractional-order oscillator. This phenomenon appears on the relationship curves of the output signal versus the noise intensity, versus the noise correlation rate, versus the fractional exponent, versus the viscous damping coefficient, as well as versus the system characteristic-frequency. In addition, the non-monotonous dependence of the output signal on the friction coefficient is also discussed.