The studies on modeling of concrete fracture by employing finite element methods have been carried out for the last thirty years. Among these constitutive models, isotropic damage concepts have been found more advantageous for its numerical practicability on modeling of concrete fracture compared to smeared crack applications. In this paper, a new damage function is proposed by simplifying the calculated curves for the damage function in a previous study. A new relation for the fracture energy of concrete is obtained by using this new damage function and the suitability of the recommended equation with the previously proposed relations is verified. Besides that, a realistic damage bounding surface for concrete elements subjected to biaxial stress states is proposed. Finally, the successful results of the applications of the damage model to a plain concrete specimen and a shear panel are illustrated.