Multiplicative noise is found to divide the growth law of tumors into two parts in a logistic model, which is driven by additive and multiplicative noises simultaneously. The Fokker-Planck equation was also derived to explain the fact that the influence of the intensity of multiplicative noise on the growth of tumor cells has a stochastic resonance-like characteristic. An appropriate intensity of multiplicative noise is benefit to the growth of the tumor cells. The correlation between two sorts of noises weakens the stochastic resonance-like characteristic. Homologous noises promote the growth of the tumor cells.