This paper presents a grasping strategy for unknown objects that imitating human grasping reflex for the anthropomorphic robot hands. A 10 months baby may bend his/her thumb and 4 fingers trying to grasp an object when it is in contact with the palm. After grasping it, if the object is plucked from the baby's hand, the baby holds the object more strongly. In addition, the hand approaches the object by only touching the palm lightly. The reaction of the hand is called a grasping reflex. In the proposed grasping strategy, each joint of the thumb and the fingers is controlled independently using the contact force affecting its adjacent fingertip side link to imitate the grasping reflex. By setting a suitable contact force, both fingertip grasping and enveloped grasping with uniform grasping force are executable. Experimental results of grasping three dimensional unknown objects by using an anthropomorphic robot hand called Gifu Hand III are shown.