During fusion welding of the Cu-containing high-entropy alloy (HEA) of CoCrFeNiCu, Cu precipitates at the grain boundary and reduces the welding quality and mechanical properties. Solid-phase diffusion welding is connected with the diffusion of elements, which reduces the segregation of Cu and solves this problem well. In the present work, the study of diffusion welding of CoCrFeNiCu HEA with 304 stainless steel (304SS) was carried by SEM, EBSD, TEM, and XRD. The properties of the microstructure and crystal type were obtained. The results show that element diffusion can achieve high-quality connection between the two metals. As the temperature increases, the diffusion capacity increases. The pores at the interface disappear. The thickness of the diffusion layer is between 10-31 μm, without forming intermetallic compound, which shows that a solid solution microstructure is formed after diffusion. According to the XRD, this microstructure is mainly as CoCrFeNiCuMn, that leads to an improvement in the mechanical properties. The hardness of the CoCrFeNiCu HEA-diffusion layer-304SS shows a gradient increase. The crystal structure type is mainly as substructured and recrystallized structure. The proportion of low-angle grain boundaries is 93% in the diffusion layer. The EBSD test results show that the grain orientation of the welded joint (diffusion layer) has changed, mostly concentrated on the (111) plane. This also causes anisotropy of the mechanical properties. Tensile performance test showed that the material fractured in the CoCrFeNiCu HEA base material area. These show that diffusion welding achieves a high-quality connection of the two materials.