This study seeks evidence on whether the return series on Tehran Stock Exchange (TSE) is independent and follows the random walk model. Two hypotheses introduced to attaining this goal. First, Price series follows the random walk model and are independent. Second, Price series of investment companies are random series. The sample primarily includes 50 active listed companies’ daily price and daily price index and Investment Company’s daily price on the TSE over the period 1999 to 2009. The results of both non-parametric (Kolmogrov—Smirnov: normality test and run test) and parametric test (Autoregressive model, ARIMA model) provide evidence that the security returns do not follow the random walk model and the significant correlation coefficient at different lags reject the null hypothesis of weak-form efficiency. In other words, investors can’t achieve extra return using historical return and price information.