To address the inherent contradiction among structural complexity, grasping force and compliance of conventional multi-fingered hands, this paper proposes a modular design methodology that synergizes the transmission advantages of linkages and tendons. The finger modules integrate rigid linkage mechanisms with tendon-spring compliant systems to achieve coupled proximal/distal phalanx motion, delivering enhanced grasping force and compliance while maintaining low systemic complexity. Through the analysis of force-displacement coupling relationships, kinematic models correlating fingertip contact forces with compliant joint rotations are established, thus quantitatively characterizing the grasp compliance. The thumb module employs a unidirectional tendon-driven mechanism, uses the mapping relationships between actuation angles and phalange rotations combined with staggered-stiffness torsional springs to ensure the grasping adaptability, minimize the volumetric footprint and achieve precise fingertip control. Modular architecture significantly streamlines manufacturing, installation and maintenance processes, thus reducing the total cost. Experimental results demonstrate that the proposed multi-fingered hand is of high compliance and adaptability. It achieves 11 precision grasps and 5 power grasps classified under the Feix Taxonomy, with a single-finger lifting capacity up to 98 N in conventional dimensions. The proposed multi-fingered hand has been successfully integrated into GAC R&D Center’s GOMATE Humanoid Robot System, which provides a high-adaptability grasping solution to humanoid service robotics.