In recent years, critical slowing down phenomenon has shown great potentials in disclosing whether a complex dynamic tends toward critical cataclysm. Based on the concept of critical slowing down, the observed data of temperature in different regions in China which have different noises are processed in this article to study the precursory signal of abrupt climate change. First, Mann-Kendall(M-K)method is used to find the locations of the abrupt climate change in different regions, then the autocorrelation coefficient which can characterize critical slowing down is calculated; the appearance-time moments of early warning signals of abrupt climate change under the influence of different noises are also stadied. The results show that for different signal-to-noise ratios, the critical slowing down phenomenon has appeared in the data 5-10 years before the abrupt climate change took place, which indicateds that critical slowing down phenomenon is a possible early warning signal for abrupt climate change and the noise has less influence on the test results for early warning signals of abrupt climate change. Accordingly, it demonstrates the reliability of critical slowing down phenomenon to test the precursory signals of abrupt climate change, which provideds an experimental basis for the wide applications of the present method in real observation data.