There has been profuse development in the stock markets all over the world in the past decades. The 21st century has seen intriguing changes in the stock markets in both developed and emerging economies. This paper examines the weak-form efficiency of listed firms on the Ghana Stock Exchange (GSE) by applying the Random Walk Hypothesis using weekly closing stock prices on the GSE from January, 2007 to June, 2012. The GSE financial market returns series exhibit volatility clustering that shows an indication of inefficiency on the GSE. The results of both the descriptive statistics of the weekly market returns and the normality tests show that returns from GSE did not follow the normal distribution. The study recommends that transaction cost should be reduced to improve the market activities of the GSE. Also, efforts should be intensified to get as many firms as possible to be listed on the stock market to enhance competition among stocks.