Existing grippers for unmanned aerial vehicle (UAV) manipulation have persistent challenges, highlighting a need for grippers that are soft, self-adaptive, self-contained, easy to control, and lightweight. Inspired by tendril plants, we propose a class of soft grippers that are voltage driven and based on winding deformation for self-adaptive grasping. We design two types of U-shaped soft eccentric circular tube actuators (UCTAs) and propose using the liquid-gas phase-transition mechanism to actuate UCTAs. Two types of UCTAs are separately cross-arranged to construct two types of soft grippers, forming self-contained systems that can be directly driven by voltage. One gripper inspired by tendril climbers can be used for delicate grasping, and the other gripper inspired by hook climbers can be used for strong grasping. These grippers are ideal for deployment in UAVs because of their self-adaptability, ease of control, and light weight, paving the way for UAVs to achieve powerful manipulation with low positioning accuracy, no complex grasping planning, self-adaptability, and multiple environments.