The development of universal grippers able to pick up unfamiliar objects of widely varying shapes and surfaces is a very challenging task. Passively compliant underactuated mechanisms are one way to obtain the gripper which could accommodate any irregular and sensitive grasping object. The purpose of the underactuation is to use the power of one actuator to drive the opening and closing motion of the gripper. The fully compliant mechanism has multiple degrees of freedom and can be considered as an underactuated mechanism. This paper presents a new design of the adaptive underactuated compliant gripper. The optimal topology of the gripper structure was obtained by two different methods simultaneously: iterative FEM optimization procedure and optimal criteria method using mathematical programming. The main points of this paper are the explanation of the new compliant gripper structure and presentation of the gripper behavior during grasping and lifting the gripping objects.