This paper uses the ARFIMA-FIGARCH model to investigate the China’s monthly inflation rate from January 1983 to October 2005. It is found that both first moment and second moment of inflation have remarkable long memory, indicating the existence of long memory properties in both inflation level and inflation uncertainty. By the Granger-causality test on inflation rate and inflation uncertainty, it is shown that the inflation level affects the inflation uncertainty and so supports Friedman hypothesis. Therefore, as for policy maker, they should roundly concerns on long memory properties of inflation and inflation uncertainty, and their single-direction relationship between them.