In this paper, estimation of second order polynomial systems’ domain of attraction (DA) via rational Lyapunov function is investigated. One of the methods for estimating DA is to find the greatest level set. In this study, in order to obtain the greatest level set, cost function based on increasing the region enclosed to the level set has been offered instead of using shape factor. Estimating DA has been converted into solving bilinear matrix inequality optimization problem. Capacity of this method compared to other methods in recent studies has been shown through some examples.