An active contour model has been used to detect the edges in a still image. In order to apply the active contour model to edge detection, the energy function which consists of internal, external and image energies should be defined. After defining the energy function, the edge of an object is detected through minimization of the value of the energy function. In this paper, the modified internal energy function is proposed to improve the convergence of the energy function when the active contour model is applied to the tracking of deformable objects using the greedy algorithm. In order to show the performance of the proposed energy function, experiments were carried out for the still and animated images.