Bio-inspired hand-like gripper systems based on shape memory alloy (SMA) wire actuation have the potential to enable a number of useful applications in, e.g., the biomedical field or industrial assembly systems. The inherent high energy density makes SMA solutions a natural choice for systems with lightweight, low noise and high force requirements, such as hand prostheses or robotic systems in a human/machine environment. The focus of this research is the development, design and realization of a SMA-actuated prosthetic hand prototype with three fingers. The use of thin wires (100 μm diameter) allows for high cooling rates and therefore fast movement of each finger. Grouping several small wires mechanically in parallel allows for high force actuation. To save space and to allow for a direct transmission of the motion to each finger, the SMA wires are attached directly within each finger, across each phalanx. In this way, the contraction of the wires will allow the movement of the fingers without the use of any additional gears. Within each finger, two different bundles of wires are mounted: protagonist ones that create bending movement and the antagonist ones that enable stretching of each phalanx. The resistance change in the SMA wires is measured during actuation, which allows for monitoring of the wire stroke and potentially the gripping force without the use of additional sensors. The hand is built with modern 3D-printing technologies and its performance while grasping objects of different size and shape is experimentally investigated illustrating the usefulness of the actuator concept.