The main purpose of this study is to ascertain the existence (or not) of a relationship between Inflation and economic growth in Nigeria. The methodology employed in this study is the cointegration and Granger causality test. Consumer price index (CPI) was used as a proxy for Inflation and the GDP as a perfect proxy for economic growth to examine the relationship. The scope of the study spanned from 1970 to 2005. A stationarity test was carried out using the Augmented Dickey-Fuller test (ADF) and Phillip-Perron test (PP) and stationary found at first difference at 1% and 5% level of significance. The Johansen-Juselius co-integration technique employed in this study proved to be superior to the Engle and Granger (1987) approach in assessing the co-integrating properties of variables, especially in a multivariate context. The result of the test showed that for the periods, 1970-2005, there was no co-integrating relationship between Inflation and economic growth for Nigeria data. Further effort was made to check the causality relationship that exists between the two variables by employing the VAR-Granger causality at two different lag periods. The results showed the same at different lags. The first test was conducted using lag two (2) and in the result unidirectional causality was seen running from Inflation to economic growth. Further test at lag four (4) was carried out and it only supported the first by also indicating a unidirectional causality running from Inflation to economic growth. Various studies as reviewed in the literature came out with the result that high inflation is and has never been favourable to economic growth. Hence, the study through the empirical findings maintain the fact that the causality that run from inflation to economic growth is an indication of relationship showing that Inflation indeed has an impact on growth.