The leaf-like origami structure is inspired by geometric patterns found in nature, exhibiting unique transitions between open and closed shapes. With a bistable energy landscape, leaf-like origami is able to replicate the autonomous grasping of objects observed in biological systems such as the Venus flytrap. We show uniform grasping motions of the leaf-like origami, as well as various nonuniform grasping motions that arise from its multitransformable nature. Grasping motions can be triggered with high tunability due to the structure's bistable energy landscape. We demonstrate the self-adaptive grasping motion by dropping a target object onto our paper prototype, which does not require an external power source to retain the capture of the object. We also explore the nonuniform grasping motions of the leaf-like structure by selectively controlling the creases, which reveals various unique grasping configurations that can be exploited for versatile, autonomous, and self-adaptive robotic operations.