Grasping unstructured and fragile objects such as food and fruits is a great challenge for robots. Being naturally different from the traditional rigid robot, soft robotics provide highly promising choices with their intrinsic flexibility and compliance to objects. Inspired by duck foot and octopus tentacle, a pneumatic webbed soft gripper was proposed, which is consisted of four multi-chambered fingers and four webs. Due to its silicone body and soft web structure, the developed soft gripper can naturally adapt, grasp and hold delicate and unstructured objects. Compressed air inflated into the three chambers of the finger actuates the silicone body and performs inflection and extension. The silicone web follows the motion of four fingers, forming a semi-closed grasping configuration. The fingers were fabricated with silicone rubber and constraint spring by casting process. The web was cast around the fingers. The inflecting motion was modeled via the pneumatic principle and geometrical analysis. The dynamic properties of the finger were tested by step and sinusoidal signals. And the grasping performances for different objects, such as egg, strawberry, candy, and knife, were also demonstrated by experiments. The proposed soft gripper performed stably in response to a 0.4 Hz reference sinusoidal signal. The bionic structure greatly improves the stability and reliability of grasping, particularly for unstructured and fragile objects. Moreover, the webs ensure the grasping for multiple objects in one snatch, especially suitable for agricultural products and food processing.