Existing soft grippers commonly face the issue of limited contact area with objects, while structures capable of large-enveloping grasps are typically characterized by complex and bulky designs, making it difficult to reconcile the need for extensive surface contact with demands for structural simplicity and compactness. To address this trade-off, a novel origami gripper was designed. Drawing inspiration from the coiling motion of snakes, the gripper utilized a motor-driven winding mechanism to pull a string, driving the sequential folding of the origami structure, thereby achieving compliant coiling grasping. Experiments were conducted to analyze the influence of parameters including origami thickness, width, length, and the origami unit adjacent-edge angle on the gripping force. The results demonstrated that the gripper achieved optimal grasping performance when the origami thickness was 0.125 mm, the origami unit adjacent-edge angle was 60°, and the diagonal width was 22 mm. The gripper not only exhibited notable adaptability to both regular and irregular objects, but also demonstrated considerable load-bearing capacity, reliably grasping objects weighing up to 500 g. Characterized by its compact size, simple structure, large enveloping contact area, and substantial gripping strength, the proposed origami gripper provides an innovative technical solution for practical applications such as automated fruit and vegetable harvesting and compliant handling.