Dimethyl ether (DME, CH3OCH3) is the simplest of ethers and is considered one of the leading candidates in the quest for a substitute for petroleum-based fuels. In this work, we analyzed the one-step synthesis of DME in a shell-and-tube type fixed-bed reactor. We have conducted simulations using a one-dimensional steady-state model of a heterogeneous catalyst bed. This model considered heat and mass transfer between the catalyst pellets and reactants and the effectiveness factor of the catalysts, together with the reactor cooling through the reactor tube wall. The reactor simulation was carried out under steady-state conditions. Thereafter, we compared the data of simulation results with the data obtained from the operation of a pilot-scale reactor and found acceptable agreement between the two data sets. Moreover, we analyzed effectiveness factors of the catalyst pellet and along the length of the reactor where we also analyzed temperature profiles and concentrations of the components. The analyses showed that complex reactions, when coupled with pore diffusion within the catalyst pellets, result in unusual values of the effectiveness factor along the length of the reactor. Given these results, the reactor demonstrated high performance for such variables as CO conversion and DME yield. On the contrary, operations over a high temperature range are unavoidable even though this type of reactor has been in general use. Eventually more effective cooling strategies in the operation of this type of reactor should be developed and studied.