This study examined whether a selected African stock exchanges provide evidence of weak form efficiency in the recent time period January 2013 to December 2015. Two objectives examined were the normality of distribution of stock prices in African stock markets; and to ascertain whether current values of the stock prices are related to various lags of the past stock prices in African stock markets. The study covered 13 out of the 28 stock exchanges in Africa, representing 38 nations' capital markets. The Jarque-bera statistics test of normal distribution and Augmented Dicker Fuller test of stationarity for stock market efficiency were employed. The data obtained from the monthly All Share Index data of the markets are log transformed to arrive at stock market returns used for the data analyses. Findings from the result indicate that (1) African stock market follows normal distribution; (2) succeeding price changes are not independent and move randomly in African stock markets. The study concluded that African stock markets are weak form inefficient within the period under study. The study therefore recommended that addressing trading frictions; promoting timely disclosure and dissemination of information to investors on the performance of listed companies; and strengthening regulatory oversight are key elements of a strategy aimed at improving the efficiency of the capital market.