This paper investigates inflation persistence by using the quantile autoregression model of Koenker and Xiao (2006) and the quantile unit root test of Koenker and Xiao (2004). The data of 20 OECD countries from 1958-2010 were employed. Our empirical result shows that inflation persistence varies with inflation for all OECD countries. Inflation is stationary and not highly persistent for low inflation, and is nonstationary and highly persistent for high inflation. This shows that inflation persistence is asymmetric across quantiles of the inflation.