This paper presents a grasping strategy of unknown objects imitating human grasping reflex for anthropomorphic robot hands. In the proposed grasping, each joint of the thumb and the fingers is controlled independently using the contact force affecting its adjacent fingertip side link. By setting a suitable contact force, both fingertip grasping and enveloped grasping with uniform grasping force are executable. Experimental results of three-dimensional unknown object grasping using an anthropomorphic robot hand, named Gifu Hand, with a distributed tactile sensor, are shown.