Generally, a modified version of limit equilibrium method can be used to evaluate a slope stability of the geosynthetic reinforced soil slopes. In most cases, resisting effects of geosynthetic reinforcement are dealt with considering an increased shear strength on the potential slip surface. However, it is not clear that the methods satisfy all three equilibrium equations. As we know, the pattern of normal stress distribution along the slip surface is the key factor in calculating the safety factor of slopes. In this study, the new slope stability analysis method in which not only reinforcing effects of geosynthetics can be considered but also all three equilibrium equations can be satisfied was proposed with assuming the normal stress distribution along the slip surface as quadratic curve with horizontal $chi-coordinate$. A number of illustrative examples, including published slope stability analysis examples for the reinforced and unreinforced soil slopes, loading test of large scale reinforced earth wall and centrifuge model tests on the geotextile reinforced soil slopes, were analyzed. As a result, it is shown that the newly suggested method yields a relatively accurate factor of safety for the reinforced and unreinforced soil slopes.