Dehydration of methanol to dimethyl ether (DME) over a commercial γ-Al2O3 catalyst was studied at the temperature interval 513–613 K, liquid hourly space velocity (LHSV) of 0.9–6.0 h−1 and pressures between 0.1 and 1.0 MPa. The effect of different operation conditions on the dehydration of methanol was investigated in an isothermal fixed bed reactor. A kinetic equation which describes a Langmuir–Hinshelwood surface controlled reaction with dissociative adsorption of methanol was found to fit the experimental results quite well. An activation energy of 62.4 kJ/mol was obtained for the catalyst. A two-dimensional reaction–diffusion model was established for a cylindrical-shaped methanol dehydration catalyst. The internal effectiveness factor and the concentration distribution of methanol in the catalyst were obtained by the finite element method in MATLAB. The reaction–diffusion model was verified by the global kinetics data. The calculation data agreed well with the experimental data, so the model can be used to describe the processes of reaction and diffusion in the cylindrical-shaped catalyst.