For an over-damped linear oscillator driven by multiplicative quadratic noise and periodic modulated noise, the exact analytical expressions of the first two moments, the amplitude and variance of the system steady-state response are obtained. We find that this system has richer dynamic behaviors than the traditional linear systems driven by linear noise; when the coefficients of the quadratic noise satisfy certain conditions, both the amplitude and the variance of the system steady-state response present stochastic resonance.