In recent years, critical slowing down phenomenon has shown great potentials in the area of disclosing whether complex dynamic system tends to critical cataclysm. Based on the concepts of critical slowing down, the observed data of pacific decadal oscillation (PDO) index and the national average monthly temperature are processed in this article to study the precursory signals of abrupt climate change. Take the abrupt climate change in a period from the late1970s to the early 1980s for example, the variances and autocorrelation coefficients which can characterize critical slowing down are calculated separately. The results show that the PDO index and the national average monthly temperature both have obviously a critical slowing down phenomenon before the abrupt climate change takes place, which indicates that critical slowing down phenomenon is a possible early warning signal for abrupt climate change. The introduction of critical slowing down theory into abrupt climate change precursory signals and study on it have practical significance and important scientific value for thoroughly understanding the abrupt climate change and for catching the precursory signals of abrupt climate change.