In grasping motion of a serial-link hand, contact forces at a proximal link are interfered with by distal forces, and are independent only on both ends of the hand. If each joint torque can be regulated to match the distribution of contact forces with that of the reference ones, a more adaptable grasping operation will be achieved. In this research, we consider the property of the serial-link mechanism and discuss the grasping control method with its mechanism. The control method proposed is based on the information from tactile sensors. The whole grasping operation can be achieved by the parallel process of feedback control on the local parts of the serial-link system. Feedback control of each local part consists of two basic actions : pinching and folding. For softer grasping operations, additional position feedback of the grasping shape is effective. The compliance of grasping operation is controllable to regulate the ratio of force and position feedback. This method is estimated by the numerical simulation and the experiments with the 7-serial-link hand mechanism.