The study of the relationship between inflation and growth is important as it provides crucial information for policy decisions. In this study, we seek to investigate the short-run and long-run relationship between inflation and growth in 3 groups of countries: high income, low income and middle income groups using the Auto Regression Distributed Lag models. The MG (Mean Group) and PMG (Pooled Mean Group) estimations are applied in this analysis. The Hausman Test is conducted to decide between the MG and PMG estimators. The panel data take the period of 1960-2012. As the result, MG estimator is preferred by all the 3 groups of countries. The results provide the dynamic relationships (short-run and the long-run relationships) between the three variables tested. The highly significant error correction term in the low income and middle income group further confirms the existence of a stable long-run relationship. The long-run relationship exists in the high income group but it is not significant. Comparisons of the results across the three groups of countries have revealed deeper information on the relationship across different income levels.