Stochastic resonance is a nonlinear effect that accounts for the optimum response of a dynamical system in an external stimulation at certain noise intensity. In this paper the phenomenon of stochastic resonance in a linear model subject under multiplicative noise is investigated. By applying the noise character and the linear system theory the explicit expression of the output amplitude gain (OAG) of the linear system is obtained. It is shown that the OAG is a non-monotonic function of the frequency of the stimulating signal and of the parameters of the system i.e.，the stochastic resonance phenomenon occurs. In addition the OAG increases monotonically with the increase of the noise strength and the noise correlation rate. By choosing appropriate parameters of the noise and the system the OAG of the system can be larger than one， i.e.，the OAG of the noisy system can be larger than that of the noise free system. The result is of certain significance in weak signal detection and provides a good supplement to conventional linear system theory.