Beside the stated concerns for this study, a lot of scholarly articles abound on the test of weak form efficiency and capital market. For that, the researchers deemed it fit to test if the Nigerian foreign exchange market follows a random walk or not. This and others led to this study, test of weak form efficiency and volatility of the Nigerian foreign exchange market with the following parametric tools; Augumented Dickey Fuller (ADF) unit root test, Pairwise Granger Causality test, Regression test, Normality/Random Walk test, ARCH-GARCH Model, the Autocorrelation cum partial autocorrelation method and Variance Ratio Test. After the analysis, all the results confirmed that the Nigerian foreign exchange market does not follow a random walk, hence weak form inefficient. No wonder the exchange rate business in Nigeria is very lucrative. The dealers always make abnormal profit at every slightest opportunity. Again, the result of the EGARCH framework found that volatility exacts negative impact on Nigerian foreign exchange market and that exchange rate volatility in Nigerian foreign exchange market is persistent. Again, that there is no asymmetric effect in the Nigerian foreign exchange market. Consequent upon the findings, the researchers suggest that the regulatory authorities of the Nigerian foreign exchange market tighten up their belt to enhancing the efficiency of the market. Again, the authority must do everything to stabilize the naira to ensure efficiency in the foreign market in Nigeria.