This paper presents impedance controllers with adaptive friction compensation for the five-finger dexterous robot hand DLR-HIT II in both joint and Cartesian space. An FPGA-based control hardware and software architecture with real-time communication is designed to fulfill the requirements of the impedance controller. Modeling of the robot finger with flexible joints and mechanical couplings in the differential gear-box are described in this paper. In order to address the friction due to the complex transmission system and joint coupling, an adaptive model-based friction estimation method is carried out with an extended Kalman filter. The performance of the impedance controller with both adaptive and parameter-fixed friction compensations for the robot hand DLR-HIT II are analyzed and compared in this paper. Furthermore, gravity estimation is implemented with Least Squares technique to address uncertainties in gravity compensation due to the close proximity and complexity of robot hand components. Experimental results prove that accurate position tracking and stable torque/force response can be achieved with the proposed impedance controller with friction compensation on five-finger dexterous robot hand DLR-HIT II.