Dexterous manipulation and grasping pose challenges for robots. Drawing inspiration from the human hand, this paper introduces a bio-inspired design for a robot finger and a robot hand, with the aim of creating an anthropomorphic robotic hand prototype. The new finger design seamlessly integrates rigid elements and soft materials. In this paper, we present a complete solution to model such bio-inspired robotic fingers leading to a real-time model-based pose controller. All five fingers of the robot hand are mounted on a carefully designed palm, with additional degrees of freedom (DoFs) for the index finger and the thumb finger to enhance dexterity. The robotic finger responds fast to control, resulting in a robotic hand capable of tracking human hand motion in real time, using a hand tracker for the hand pose. The robotic hand can be controlled to achieve most human grasp types. Several manipulation and grasping tasks are demonstrated using teleoperation.