As long as financial markets are concerned, for many years' economists, statisticians and financial analyst have been interested in developing and testing models of stock price behaviour and their forecast. This study examines whether the Kuala Lumpur Stock Market, Malaysia is efficient if the Stock Returns follow a random walk. The study employs daily closing prices of Kuala Lumpur Stock Exchange - Bursa Malaysia Composite Index for a time period of 28 Apr 1998 to 30 Dec 2014. The existence of random walk for Bursa Malaysia Index has been examined through autocorrelation, Q-statistics and the run test and finds that the Kuala Lumpur Stock Market was not efficient in the weak form during the testing period. The results suggest that the stock prices in Malaysia do not reflect all the information in the past stock prices and abnormal returns can be achieved by investors through exploiting the market inefficiency.