This study, using end of the month stock market index investigated the efficiency of the Nigerian stock market employing unit root test, and standard GARCH (1,1) model as major alternate form methods. The simple descriptive statistics was necessarily used for snapshot decisions.The unit root test and the GARCH model proved that the Nigerian stock market follows a random walk process while a wider informational determining test-the Granger causality showed that the market as far as information is concerned is not semi-strong efficient. The descriptive statistics and the GARCH model showed that the Nigeria stock market is volatile implying that there exists a high level of risk in stock trading in Nigeria. However, the result suggested a low persistence of volatility clustering for the market indicating that increase in volatility is not likely to remain high over several periods.The researcher therefore made some recommendations such as restricting the debt/equity ratio, palliating further the listing requirements, establishing a functional derivatives market to boost the market size,assuring effective information dissemination and awareness to forestall sluggish market behavior.