The inclusion of sacrificial hydrogen bonds is crucial for advancing high-performance rubber materials. However, the molecular mechanisms governing the impact of these bonds on material properties remain unclear, hindering progress in advanced rubber material research. This study employed all-atom molecular dynamics simulations to thoroughly investigate how hydrogen bonds affect the structure, dynamics, mechanics, and linear viscoelasticity of rubber materials. As the modified repeating unit ratio (β) increased, both interchain and intrachain hydrogen bond content rose, with interchain bonds playing a predominant role. This physical cross-linking network formed through interchain hydrogen bonds restricts molecular chain movement and relaxation and raises the glass transition temperature of rubber. Within a certain content of hydrogen bonds, the mechanical strength increases with increasing β. However, further increasing β leads to a subsequent decrease in the mechanical performance. Optimal mechanical properties were observed at β = 6%. On the other hand, a higher β value yields an elevated stress relaxation modulus and an extended stress relaxation plateau, signifying a more complex hydrogen-bond cross-linking network. Additionally, higher β increases the storage modulus, loss modulus, and complex viscosity while reducing the loss factor. In summary, this study successfully established the relationship between the structure and properties of natural rubber containing hydrogen bonds, providing a scientific foundation for the design of high-performance rubber materials.