The invention describes a robot gripper having a fixing flange (1) for detachably attaching it to a robot manipulator arm, and at least one actuator element (5), which is supported in a frame (3) and actuates at least two gripper jaws (15, 18) indirectly or directly kinematically via at least one articulated unit (2). The invention is characterized by the fact that at least the fixing flange, the frame and the actuator element are manufactured integrally using a generative manufacturing method, and by the fact that the actuator element is in the form of a bellows, encloses an internal volume (6), which can be filled with a medium via at least one opening, and is capable of expanding, when filled with the medium, along a linear axis (A, B) predetermined by the bellows design of the actuator element and of contracting, when the volume is emptied, in the opposite direction along the linear axis.