Although exfoliating graphite to give graphene paves a new way for graphene preparation, a general strategy of low-boiling-point solvents and high graphene concentration is still highly required. In this study, using the strategy of tailoring Hansen solubility parameters (HSP), a method based on exfoliation of graphite in water/acetone mixtures is demonstrated to achieve concentrated graphene dispersions. It is found that in the scope of blending two mediocre solvents, tailoring the HSP of water/acetone mixtures to approach the HSP of graphene could yield graphene dispersions at a high concentration of up to 0.21 mg ml{sup -1}. The experimentally determined optimum composition of the mixtures occurs at an acetone mass fraction of {approx}75%. The trend of concentration varying with mixture compositions could be well predicated by the model, which relates the concentration to the mixing enthalpy within the scope of HSP theory. The resultant dispersion is highly stabilized. Atomic force microscopic statistical analysis shows that up to {approx}50% of the prepared nanosheets are less than 1 nm thick after 4 h sonication and 114g centrifugation. Analyses based on diverse characterizations indicate the graphene sheets to be largely free of basal plane defects and oxidation. The filtered films are also investigated in terms of their electrical and optical properties to show reasonable conductivity and transparency. The strategy of tailoring HSP, which can be easily extended to various solvent systems, and water/acetone mixtures here, extends the scope for large-scale production of graphene in low-boiling-point solutions.