Time-delayed Logistic system driven by correlated Gaussian white noises could be a more true reflection of the growth of tumor cell population. In this paper, we study the Logistic system through the small time delay approximation to obtain the probability density of the system in its steady state, and further analyze the influences of the additive and multiplicative noise intensity, the noise-correlated time and the time delay on the steady-state probability density. The non-equilibrium phase transition phenomena induced by the noises is also studied.