The Study Investigate the relationship between economic growth (GDP) and some financial deepening indicators (money supply and credit to private sector), using a data obtained from the Central Bank of Nigeria (CBN) statistical bulletin for the period 1981-2012. The study employed the conventional augmented dickey fuller test to test for stationarity among the three variables ( GDP, money supply and credit to private sector, Johensen cointegration technique to determine the order or the cointegrating equation. Granger causality test was used to check for causal relationship among the variables (i.e uni-directional, bi-directional or feedback) and then the Vector Error Correction to check for a short-run or long-run relationship among the three variables. The results indicate that all the three variables are non-stationary at levels, but became stationary after first differencing once. The three variables are cointegrated with at most one ciontegrating equation, b-bidirectional causality runs among the three variables. The VECM suggested a long-run relationship among the three.