This paper describes grasp stability for a multi-fingered robot hand, called the KIST hand. The robot hand has controlled by four under-actuated fingers with totally nine DOFs, which are controlled by two linear actuators and linkage knuckles. This mechanism is able to generate high power compare to common robot hands that use rotary actuators. The robot hand has four tactile sensors which are attached to the fingertips on the each finger. The each tactile sensor can independently measure the contact force between the robot hand and an object. Using the tactile sensors, various objects can be grasped, such as a small tennis ball, a plastic ball and a rubber ball. In the former part of the paper, the mechanical design of the robot hand is presented. In the latter part of the paper, the control algorithm is described, and the analysis of grasp stability is confirmed by the experimental result.