This paper presents a full-body compliant motor control strategy with a virtual musculoskeletal system for anthropomorphic robots. This integrates a task-space control module and a joint stiffness control module on joint torque control implementation. The passivity-based task-space controller manages the Cartesian forces and provides the robot with full-body compliance and balancing ability, and the joint stiffness controller locally stabilizes the desired posture trajectories. We discuss the advantage of the proposed strategy from two practical computational points of view: computational cost in the postural maintenance and redundancy resolution to suppress the internal motions. The implementation issues of the torque controller with hydraulic actuators are also discussed. The effectiveness of the proposed method is empirically validated by four kinds of full-body motion control experiments on our hydraulic biped anthropomorphic robot.