Three kinds of sandwich beams were prepared, which were cross, double cross and square sandwich structure (CSS, DCSS and SSS), using spruce wood as face panels, KH-560 modified jute fabrics reinforced epoxy laminated composites (JFRELC) as cores. This research investigated the mechanism of micro-surface modification of composites, the bending behaviors and failure modes of sandwich structures. The results showed that the grafting of KH-560 on jute fabric improved the interfacial compatibility and mechanical properties of laminated composite. The stretching vibration peak of COSi/Si-O-Si groups of the KH-560 modified composites were found. The content of silicon in the modified composites was about 4 times of that in the unmodified composite. The flexural rigidity, shear rigidity, shear modulus and shear strength of SSS were 2.10 × 108 N·mm2, 1.97 × 105 N, and 143.94 MPa, 0.948 MPa respectively, which were significantly better than that of DCSS and CSS. The load-mass ratio of short beam of DCSS was similar to the long beam of SSS. The failure modes of three grid sandwich structures included shear failure, general shear failure, indentation, panel fracture and separation between the core and panel. The failure mechanism of the shear failure cores contained fiber pulling out and fiber splitting.