Stock markets are vital to a country’s economic growth on condition that they are efficient. Examination of the efficiency of the stock market is therefore important as it provides a means for understanding the structure and hence the role of the stock market in the economy. This study tests the weak form and the semi-strong form of the Efficient Market Hypothesis (EMH) by employing multiple statistical tests of the Random Walk Model and also by testing one of the market anomalies on the Malawi Stock Exchange(MSE). The empirical findings derived from the statistical tests of the Random walk model conclusively reject the null hypothesis of the existence of a random walk for the Malawi All Share Index (MASI) and therefore it can be concluded that the Malawi Stock Exchange is not weak form efficient. The study also found that there is enough evidence to accept the hypothesis that stock prices do not immediately incorporate earnings announcement information on the Malawi Stock Exchange, which implies that the Malawi Stock Exchange is not semi-strong efficient.