The major aim of this research is to achieve a more appropriate investment model in portfolio selection for risk taker investors. In this research Markowitz model is the base for comparison in the Portfolio theory, which can construct an optimum portfolio on the basis of the special assumptions. In the present study, along with Markowitz model, the created models through the Artificial Neural Networks (ANN) are applied. Then they have been compared with Markowitz model in several cases of investment. The learning pattern for neural networks is “back propagation”. The portfolios consist of twenty shares in the Tehran Stock Exchange (www.tse.ir), which has been studied for a period of thirteen months. In both Markowitz and ANN portfolios, there is a significant difference between the daily return and the outcome of the investment at the end of the investment period in the test set. Both of these two models are statically and dynamically applied, and in both cases the neural networks’ portfolios outweighed the Markowitz’s portfolios. In this research, the suggested portfolios are for the risk takers and the major goal is to maximize the portfolios’ return. The risk of the portfolios constructed by the neural networks is less than those of the Markowitz model. Furthermore, the transaction costs have not been computed in the Markowitz and neural networks. This study shows that employment of neural networks in portfolios selection can be effective.