The vast majority of efficient market research to date has focused on the major United States and European securities market. Far fewer have investigated the developing and less developed countries markets; and no study on this area has been performed on the Dhaka Stock Exchange (DSE). The study seeks evidence supporting the existence of at least weak-form efficiency of the market. The sample includes the daily price indices of all the listed securities on the DSE for the period of 1988 to 1997. The hypothesis of the study is whether the Dhaka Stock Market is weakform efficient. The results of both non-parametric (Kolmogrov –Smirnov normality test and run test) test and parametric test ( Auto-correlation test, Auto-regression, ARIMA model ) provide evidence that the share return series do not follow random walk model and the significant autocorrelation co-efficient at different lags reject the null hypothesis of weak-form efficiency. The results are consistent in different sub-sample observations, without outlier and for individual securities. The issues are important to security analysts, investors and security exchange regulatory bodies in their policy making decisions to improve the market condition. This study deserves a continuous research on this area to reach an ultimate conclusion about the level of efficiency of less developed market.