Dynamic control of a three-fingered robot hand manipulating an object in 3D space, while allowing one of the three fingers to slide in order to change its grasp location on the object surface, is formulated. The static and dynamic friction between the sliding finger and the object surface are explicitly considered and their effects regarding the behavior of the finger and object are discussed. Motion equations of the whole system are derived and a dynamic control law for realizing the desired object motion, as well as the desired finger sliding and the desired grasping force, is proposed. The realizability of the given trajectories under the constraints of maximal static friction and dynamic friction at the grasp points, and of joint driving torque, are also discussed. A simulation example to demonstrate the use of the proposed control law is given. The results of this work will have useful application to a multifingered robot hand in performing certain tasks involving the re-grasping and re-orientation of an object without interrupting the grasp.