Understanding the mechanism of adsorption and self-assembly of surfactants on graphene is highly important to perform better optimization of the graphene dispersion process. Because of Gemini surfactants' special structure, they have a high charge capacity, high hydrophobicity, and unique self-assembly properties compared to single-chain surfactants. Therefore, Gemini surfactants with their small concentrations are expected to disperse and stabilize graphene nanosheets in aqueous solutions more effectively. We conducted molecular dynamics simulations to study adsorption and self assembly of single-chain cationic surfactant dodecyltrimethylammonium bromide (C(12)TAB) and its same family Gemini surfactant dimethylene-alpha,beta-bis(dodecyldimethylammonium bromide) ([12-2-12]Br-2) on graphene nano sheets. The results showed that assemblies morphology formed on graphene is affected by surfactant structure. We observed that increasing surface coverage, especially for [12-2-12]Br-2, leads to a transmission in adsorption mechanism and most [12-2-12]Br-2 head groups tend toward the aqueous phase and prevent water molecules from accessing graphene surface. It can be concluded from morphological assessments that [12-2-12]Br-2 is more effective than C(12)TAB in stabilizing graphene aqueous suspensions. Moreover, we investigated the effect of graphene sheet size and Gemini surfactant spacer length on the structure of surfactant assemblies on graphene. The present study results can expand our comprehension of dispersion mechanism of graphene nanosheets by Gemini surfactants.