In this paper after a general literature review on the concept of Efficient Frontier (EF), an important inadequacy of the Variance based models for deriving EFs and the high necessity for applying another risk measure is exemplified. In this regard for this study the risk measure of Lower Partial Moment of the first order is decided to replace Variance. Because of the particular shape of the proposed risk measure, one part of the paper is devoted to development of a mechanism for deriving EF on the basis of new model. After that superiority of the new model to old one is shown and then the shape of new EFs under different situations is investigated. At last it is concluded that application of LPM of the first order in financial models in the phase of deriving EF is completely wise and justifiable.