In this paper, a novel self-adaptive underactuated robot hand with rigid-flexible coupling fingers (SAU-RFC hand) is proposed. The seven degrees of freedom (DOFs) SAU-RFC hand is driven by four servomotors, consists of three fingers, including two side-turning (ST) fingers and one non-side-turning finger. Specially, the ST fingers can perform synchronous reverse rotation laterally with each other. Each finger with three joints and two DOFs introduces a flexible structure, and the inner part of the proximal phalanx that makes most of the contact with the object is replaced by a flexible belt. The fingers can generate flexion/extension under the pull of the flexible belt, and the middle and distal phalanxes are mechanically coupled through a four-bar linkage. In particular, the flexible belt in the inner direction of the finger will deform, while it will not deform in the outer direction since the outer is a rigid structure. The flexible belt not only plays the role of transmitting power but also has the effect of uniformizing the contact force. Due to the rigid-flexible finger structure, the developed robot hand has a higher self-adaptive grasping ability for objects with different shapes, sizes, and hardness. In addition, the kinematic and kinetic analyses of SAU-RFC hand are performed. A contact force distribution model is established for the flexible belt, which demonstrates its effect of promoting uniform force distribution theoretically. In the end, experiments are conducted on different objects to verify the performance of SAU-RFC hand.