Like several other countries both industrialised and non-industrialised, one of the central objectives of macroeconomic policies in Tanzania is to promote economic growth and to keep inflation at a low level. However, there has been substantial debate on whether inflation promotes or harms economic growth. Motivated by this controversial, this study examined the impact of inflation on economic growth and established the existence of inflation growth relationship. Time-series data for the period 1990 -2011 were used to examine the impact of inflation on economic growth. Correlation coefficient and co-integration technique established the relationship between inflation and GDP and Coefficient of elasticity were applied to measure the degree of responsiveness of change in GDP to changes in general price levels. Results suggest that inflation has a negative impact on economic growth. The study also revealed that there was no co-integration between inflation and economic growth during the period of study. No long-run relationship between inflation and economic growth in Tanzania.