In recent years, critical slowing down phenomenon has shown great potentials in disclosing whether a complex dynamic tends to critical cataclysm. Based on the concepts of critical slowing down, the observed data of temperature and the pacific decadal oscillation (PDO) index and the intensity of Aleutian low pressure, which have different noises are processed in this article to study the precursory signals of abrupt climate change. Take the abrupt climate change in the late1970s-early 1980s as an example, then variances and autocorrelation coefficients which can characterize critical slowing down will be calculated separately; the occurring time of precursory signal of abrupt climate change under the noises influence is studied. The results show that the critical slowing down phenomenon appears in the data with different signal-to-noise ratios before the abrupt climate change takes place, which indicates 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 precursory 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 provides an experimental basis for the wide applications of the present method in real observation data.