The invention discloses an enveloping under-actuated robot gripper. The enveloping under-actuated robot gripper can solve the problems that an existing mechanical robot gripper has large movement stroke, a complex mechanism, and large number of parts. The enveloping under-actuated robot gripper comprises a driving motor, a base, a driving seat, a driving pad, a connecting key for a motor and a movable base, four claw plates, four connecting rod kinematic chains for connecting the claw plates and the driving seat, a driving seat connecting rod, a bearing connecting rod, and a clamping jaw connecting rod, wherein the driving seat and the driving pad are fixedly connected to the driving motor to form a first-level fixing mechanism; and the moving base and the four claw plates are connected toform a second-level moving mechanism. When the gripper works, the rotation movement of the driving motor is transferred to the second-level moving mechanism through the connecting key to realize theenveloping and unfolding of the moving gripper. The connecting rod kinematic chains use the direction change of the rotation axis to ensure that the distance between two levels of platforms remains unchanged, and can convert 6 degrees of freedom into 1 degree of freedom. The enveloping under-actuated robot gripper has a simple and reliable structure, clever configuration, and few driving sources,and is suitable for application scenarios such as grabbing and picking of fruits and vegetables.