In the present paper, the phenomena of stochastic resonance (SR) for a stochastic cancer development system that is driven by correlated multiplicative and additive noises is investigated. By using the fast descent method and the two-state theory, the expression of the signal-to-noise ratio (SNR) is obtained. Numerical results show that conventional SR occurs in the cancer growth model under different values of the system parameters. If the correlation strength between the two noises is positive or negative, the effects of the addictive noise intensity, the multiplicative noise intensity, and the correlated noise strength on the SNR are different.