This paper highlights the problem of inflation volatility in Australia and deploys quarter‐on‐quarter CPI‐inflation data over the period 1949q3–2013q4 to investigate the proposition of a feedback relation between inflation and inflation volatility in this country. The paper adopts the generalised autoregressive conditional heteroskedastic (GARCH) modelling technique to estimate simultaneously the conditional mean and the conditional variance of inflation and their interrelations in a dynamic context. A bivariate Granger‐causality test is then conducted to determine whether a causal relation exists between inflation and inflation volatility, as measured by the estimated conditional variance of inflation. The empirical results suggest the presence of a feedback relation between inflation and inflation volatility with a positive (adverse) impact of inflation volatility on the rate of unemployment. A second finding of the paper, based on the preferred exponential GARCH (1,1) model, is that inflation shock has an asymmetric impact on inflation volatility. A negative (downward) inflation shock is found to have a larger effect on the log of the conditional variance of inflation than the effect of a positive inflation shock of the same magnitude. These are the key findings of the paper. The concluding section summarises its other findings and draws some of the implications for Australian monetary policy.