In this paper, the stochastic resonance in a periodic potential system driven by correlated multiplicative and additive white noises is studied. Using the linear response method, the expressions of power spectral density, amplitude of response and phase difference of response are given. The effects of noises on stochastic resonance are also presented. It is found that stochastic resonance occurs by adjusting the intensity of multiplicative noise for small noise. Moreover, the value as well as the plusminus sign of the correlation between the additive and multiplicative noises have slight influence on the amplitude and phase difference of system response. The curves of amplitude and phase difference of response both exhibit a peak when the intensity of multiplicative noise is small, stochastic resonance occurs and energy transfers from noise to signal. With the increase of multiplicative noise intensity, stochastic resonance disappears and the noise makes system from order to disorder.