The conversion of dimethyl ether(DME) has been carried out over $\gamma-alumina$, silica-alumina, and modified $\gamma-aluminal$ catalysts. Especially, the water effect has been investigated on purpose to develop a suitable catalyst for one-step synthesis of DME from $CO_2$ hydrgenation, The $\gamma-Al_2O_3$ modified with 1 wt% silica is more active and less deactivated by water than unmodified one. $CO_2has$ no effect on catalytic dehydration of methanol to DME.