Determining an appropriate grasp configuration for multi-finger grasping is difficult due to the complexity of robotic hands. The multi-finger grasp planning should consider not only geometry constraints of objects but also kinematics and dynamics of robotic hand. In this paper, a precision grasp-planning framework is presented for multi-finger hand to grasp unknown objects. First, the manipulation capabilities of the robotic hand are analyzed. The analysis results are further used as bases for the precision grasp planning. Second, the superquadric (SQ) fitting method is used for approximating unknown object models. Finally, a local–global optimization method is implemented to find appropriate grasp configurations for dexterous hand. The presented planning framework is validated in simulation experiments. Simulation results demonstrated that the presented grasp-planning framework enables the multi-finger hand to grasp unknown objects effectively.