This study has been conducted to explore the subject Efficient Market Hypothesis. Various researches have been done on efficient market hypothesis in American Stock Exchange, New York Stock Exchange&some researches have also been done in Indian Stock Exchange. The efficient market hypothesis has been widely tested and, with few exceptions, found consistent with the data in a wide variety of markets: the New York and American Stock Exchanges, the Australian, English, and German stock markets, various commodity futures markets, and the Over-the-Counter markets. The purpose of this paper is to investigate the weak-form efficiency of the Indian Stock Market-Bombay Stock Exchange (BSE). This study is a step ahead to test the market hypothesis in the Bombay Stock Exchange. Various tests related to weak form of market hypothesis were also applied on the 30 companies used in the formation of index of Bombay Stock Exchange i.e. Sensex to check the efficiency level of Bombay Stock Exchange (BSE). This study is intended to be a useful contribution to students and researchers of investment management. It is intended to provide a link between theory and practice and an opportunity to test theoretical ideas regarding the influence of various types of previously available information on share prices. Run test and auto correlation has been applied on share prices to check the weak form of efficiency, and the results reveal that Bombay Stock Exchange is weak form efficient.