Aiming at the problem that the nonlinear characteristics of climate system make it difficult to predict/early warn the abrupt change of climate, this paper starts from the long-range correlation of climate system, and uses the zero dimensional climate model and two folding models to study whether the long-range correlation of a dynamic system has some general change law when it slowly approaches its critical turning point. Results show that the Hurst index, which represents the long-range correlation of the three bifurcation models, increases continuously (significance level α=0.05) when they approach their critical tipping points, which indicates that monitoring and detecting the change of the long-range correlation of the climate system can provide useful information for the early warning of the tipping points of the climate system.