Soft grippers are key manipulation tools for robotics and end effectors for securely grasping objects of various shapes and sizes on demand. However, critical challenges, including self-adaptive grasping to curved surfaces and monitoring the contact state, remain. Here, a gecko-inspired curved flexible surface adaptive gripper (CSAG), which consists of a variable-bending pneumatic actuator, a triboelectric sensor (T-sensor), and a gecko-inspired microwedge adhesive, is proposed. The contact-sensitive triboelectric sensor can sense the critical contact state of objects to trigger a variable-bending pneumatic actuator with sufficient shear loading for the geckoinspired microwedge adhesive. A set of experiments are implemented to verify that the proposed soft gripper can adaptively grasp diverse curved objects, including quail eggs, cans, shuttlecocks, expanding objects with varying volumes (such as balloons, the range of diameter variation is 20–115 mm), and spherical acrylic cylinders (20–40 mm) at low pressures (20–25 kPa) with a maximum weight of 37 g. Additionally, the tracking and grasping of a moving ball is demonstrated via a mean-shift algorithm based on image recognition coupled with coordination tracking of a robotic arm. The soft gripper provides a new paradigm to achieve switchable grasping of curved flexible surfaces, which broadens future applications for versatile unstructured human‒robot‒environment interactions, such as adaptive robots and medical devices.