This paper takes the typical chaotic system， the Lorenz system， as the subject. We use the detrended fluctuation analysis method to study the systems long-range correlation for different initial values and parameters. It turns out that the systems long range correlation is related with its initial values phase space position. When the initial value is close to the unstable equilibrium points， the systems long rang correlation is strengthened， the scaling exponents α are bigger， and the predictability of the system is better. When the system is in complete chaotic state， its long range correlation becomes weak with the parameters increasing， and the scaling exponents α are decrease， the predictability of the system becomes weaker. This reveals the relationship between the systems long range correlation and its predictability. We disturbed the system equation with random noise and found that the systems long range correlation decreases with the increase of random noise intensity. This result further signifies out that the Lorenz system's long range correlation is a physical parameter that may serves as an effective predictability criterion.