This paper presents the analysis of grasp stability for a bio-mimetic robot hand by using polygon segmentation algorithm. The presented hand has four independency moving fingers, which are driven by four-coupled link mechanism with two linear actuators. The robot hand was designed considering the dexterity and the compact size suited for various objects in daily life. Tactile sensors are mounted on the palm and the fingertip at each finger of the hand. With tactile sensor based on feedback control, the paper explains the control of the hand which is very stable in grasping by using new algorithm called polygon segmentation algorithm. This algorithm can be appiled for the analysis of grasp stability to various objects regardless of the number of contact points. Using the force equilibrium points and vertex of the polygon, several triangles can be obtained. We can obtain the polygon segmentation algorithm by analyzing the relationship among triangles. In order to verify this algorithm, experiments were conducted by using three types of objects with different characteristics.