Robots are playing an increasingly important role in engineering applications. Soft robots have promising applications in several fields due to their inherent advantages of compliance, low density, and soft interactions. A soft gripper based on bio-inspiration is proposed in this study. We analyze the cushioning and energy absorption mechanism of human fingertips in detail and provide insights for designing a soft gripper with a variable stiffness structure. We investigate the grasping modes through a large deformation modeling approach, which is verified through experiments. The characteristics of the three grasping modes are quantified through testing and can provide guidance for robotics manipulation. First, the adaptability of the soft gripper is verified by grasping multi-scale and extremely soft objects. Second, a cushioning model of the soft gripper is proposed, and the effectiveness of cushioning is verified by grasping extremely sharp objects and living organisms. Notably, we validate the advantages of the variable stiffness of the soft gripper, and the results show that the soft robot can robustly complete assemblies with a gap of only 0.1 mm. Owing to the unstructured nature of the engineering environment, the soft gripper can be applied in complex environments based on the abovementioned experimental analysis. Finally, we design the soft robotics system with feedback capture based on the inspiration of human catching behavior. The feasibility of engineering applications is initially verified through fast capture experiments on moving objects. The design concept of this robot can provide new insights for bionic machinery.