In this paper, an anthropomimetic design of a 7-DOF dexterous robotic arm is proposed. Similar to the human arm, the arm consists of three sequentially connected modules, i.e., a 3-DOF shoulder module, a 1-DOF elbow module, and a 3-DOF wrist module. All three arm modules are also driven by cables in order to mimic the driving scheme and functionality of the human muscles. This paper addresses three critical design analysis issues, i.e., the displacement analysis, the tension-closure analysis, and the workspace analysis. A closed-form solution approach is presented for the forward displacement analysis, while the inverse displacement solution is obtained through an efficient optimization algorithm, in which both task-decomposition and dimension-reduction techniques are employed. An effective tension-closure analysis algorithm is also formulated based on the theory of convex analysis. The orientation workspace for the 3-DOF shoulder and wrist modules are then analyzed using a new equi-volumetric partition scheme based on the intuitive Tilt-and-Torsion angle parameterization. An optimization approach is then investigated for the kinematic design of the three joint modules, in which the design objective is to maximize the matched workspace of the robotic arm joints with that of the human arm joints. A research prototype of the 7-DOF cable-driven robotic arm has also been developed in order to demonstrate the anthropomimetic design concept. With a lightweight structure of 1 kg, the cable-driven robotic arm can carry a payload of 5 kg and has motion repeatability of±2.5mm.