Grasping multiple object types (versatile object grasping) with a single gripper is always a challenging task in robotic manipulation. Different types of grippers, including rigid and soft, have been developed to try to achieve the task. However, each gripper type is still restricted to specific object types. In nature, many insects can be observed to use only one tarsus mechanism to cope with several tasks. They have a very high grasping capability with objects and can adhere to a variety of surface types. Inspired by insect tarsus, this paper proposes a novel underactuated, single cable-driven, compliant gripper design. The structure of the gripper is based on the hornet tarsus morphology with a proportional scale. An additional pulley-like structure is introduced to increase the generated grasping torque. To maintain the ability to automatically rebound back to the original position, a torsion spring is implemented at each joint. In order to stably grasp and hold objects, soft adhesive pads with an asymmetric sawtooth-like surface structure are attached at the tarsus segments. The performance of this insect tarsus-inspired gripper with the soft pads is evaluated by grasping 35 different objects of various sizes, shapes, and weights for comparison with industrial soft and rigid grippers. The proposed gripper shows a 100% success rate in grasping all objects, while the soft and rigid gripper success rates are 81.90% and 91.43% on average, respectively. We finally demonstrate the use of our gripper installed on a robot arm for pick-and-place and pouring tasks.