The properties of model solutions consisting of a solute --- single curcumin molecule in water, methanol and dimethyl sulfoxide solvents have been studied using molecular dynamics (MD) computer simulations in the isobaric-isothermal ensemble. The united atom OPLS force field (OPLS-UA) model for curcumin molecule proposed by us recently [J. Mol. Liq., 2016, 223, 707] in combination with the SPC/E water, and the OPLS-UA type models for methanol and dimethyl sulfoxide have been applied. We have described changes of the internal structure of the solute molecule induced by different solvent media in very detail. The pair distribution functions between particular fragments of a solute molecule with solvent particles have been analyzed. Statistical features of the hydrogen bonding between different species were explored. Finally, we have obtained a self-diffusion coefficient of curcumin molecules in three model solvents.