The sensory function is crucial for achieving precise feedback control and environmental interaction in soft robots. Therefore, the multimodal sensory capabilities that mimic human fingers have always been a research hotspot. This study proposes a design method for a soft robotic gripper that can emulate the multimodal perception mechanism of human fingers and achieve high-precision recognition of grasped objects using machine learning algorithms. In addition, a finger texture structure inspired by human fingerprints is designed using a negative pressure-induced buckling method to enhance the soft gripper's ability to perceive minute surface textures. Inspired by slow adapting (SA) receptors and fast adapting (FA) receptors of human fingers, we have innovatively designed a capacitive curvature sensor (CS) and a triboelectric texture sensor (TS) to detect the size, material, and texture of objects. Furthermore, a non-contact medium identification sensor (MIS), having a sensitivity of more than 1300 times higher compared to the traditional MISs, is fabricated using the principle of electromagnetic resonance. It is shown that by employing a deep learning-based multi-channel feature fusion network, the soft grasping system with multimodal sensing has achieved a recognition accuracy of 98.43 % for different objects. This work provides an innovative approach for the application of soft robots in various fields, such as logistics sorting and food safety.