The long rang Coulomb on-site repulsion between π electrons in hydrogen (H) adsorbed graphene has been studied based on DFT + U calculations. This study demonstrates that the rigidity of π electronic structure of graphene is partially destroyed in the cases of H adsorption due to the introduction of un-paired electron in this system. The softness of π conjugation is largely depending on the concentrations as well as the periodicity of H adsorption. Due to the destruction of the rigidity of π conjugation, the Coulomb on-site repulsion increases. The results show that the Coulomb on-site repulsion between π electrons is very sensitive to the periodicity of H adsorption. A considerable enhancement of Coulomb on-site repulsion occurs for the systems with 3n×3n peroidcity. More importantly, the strength and the patts of Coulomb on-site repulsion in the graphene plane are significantly size-dependent, which further induces the band gap opening at Fermi level. Especially for ×6 6 system, the on-site repulsion induces a stabilized non-ferromagnetic state. Our results reveal for the first time that the considerable long rang Coulomb on-site repulsion between π electrons exists which plays an important role in the electronic characteristics of H adsorbed graphene. The finding in this investigation provides new insight into the many-body interaction between localized impurities with delocalized π electrons in graphene related materials.