The behavior of the financial market indices shows the randomness of the regions and the certainty of the public. Financial markets can be considered as non-linear dynamic systems that consider the interactions between factors in the process of immediate information analysis. The fractal market hypothesis assesses the stability and ability of financial markets to absorb shocks, in addition to testing efficiency. Numerous studies have tested the fractal market hypothesis in international financial markets, but a few studies has been denoted to the Tehran stock market. In this paper, the stock price of Tehran Stock Exchange companies has been evaluated during the period of 1393-1397 and in monthly intervals to determine whether these variables have multi-fractal characteristics in their behavior or not. An estimate of the modified R/S model has been employed to achieve the goal. The results of the above tests indicate that the stock price has a multi-fractal property and has a long-term memory in the period under review, which also implicates in the weak performance hypothesis. In fact, the random walk theory in stock prices has not been validated, and the past information can provide significant correlation with future stock price information.