The human arm exhibits remarkable capabilities, including both explosive power and precision, which demonstrate dexterity, compliance, and robustness in unstructured environments. Developing robotic systems that emulate human-like operational characteristics through musculoskeletal structures has long been a research focus. In this study, we designed a novel lightweight tendon-driven musculoskeletal arm (LTDM-Arm), featuring a seven degree-of-freedom (DOF) skeletal joint system and a modularized artificial muscular system (MAMS) with 15 actuators. Additionally, we employed a Hilly-type muscle model and data-driven iterative learning control (DDILC) to learn and refine activation signals for repetitive tasks within a finite time frame. We validated the anti-interference capabilities of the musculoskeletal system through both simulations and experiments. The results show that the LTDM-Arm system can effectively achieve desired trajectory tracking tasks, even under load disturbances of 20 % in simulation and 15 % in experiments. This research lays the foundation for developing advanced robotic systems with human-like operational performance.