The possible paths of dimethyl ether (DME) synthesis from methanol over hydrated -Al2O3(110) in vacuum and liquid paraffin have been investigated by using density functional theory (DFT). Over hydrated -Al2O3(110), the three possible paths of methanol dehydration to DME have been investigated by the DFT method in vacuum and liquid paraffin. DME synthesis from methanol is carried out along the same pathway 2CH3OH(g) 2* 2CH3OH* 2CH3O* 2H* CH3OCH3* H2O* in vacuum and liquid paraffin, and the step of highest energy barrier is the reaction of 2CH3O* CH3OCH3* O*. The energy barrier of the step in liquid paraffin is higher than that in vacuum by 0.33eV. The surface acid strength in liquid paraffin decreases over -Al2O3(110) surface comparing with vacuum, showing that stronger surface acid strength benefits to DME synthesis. Our result is in consistent with the experiment results. DME synthesis from methanol is carried out along the same pathway 2CH3OH(g) + 2* → 2CH3OH* → 2CH3O* + 2H* → CH3OCH3* + H2O* in vacuum and liquid paraffin. The highest energy barrier is the reaction of 2CH3O* → CH3OCH3* + O*, and the energy barrier of the step in liquid paraffin is higher than that in vacuum by 0.33eV. The surface acid strength in liquid paraffin decreases over -Al2O3(110) surface comparing with vacuum, showing that stronger surface acid strength benefits to DME synthesis. [ABSTRACT FROM AUTHOR]