MCM‐41, Y, ZSM‐5, and β zeolite‐supported copper catalysts prepared by the incipient wetness impregnation method were used for the coupling reaction between methanol dehydrogenation and maleic anhydride hydrogenation in a fixed bed reactor. The Cu/MCM‐41 catalyst with low acidity favoured methanol dehydrogenation to methyl formate and maleic anhydride hydrogenation to γ‐butyrolactone, while Cu/Y, Cu/ZSM‐5, and Cu/β catalysts with high acidities favoured methanol dehydration to dimethyl ether and the formation of dimethyl succinate. When the coupling reaction over the Cu/MCM‐41 catalyst was carried out at 240–300 °C, the selectivities of methyl formate and γ‐butyrolactone reached 88 % and 72 %, respectively. The coupling reaction over the Cu/MCM‐41 catalyst had good compensation for hydrogen and reaction heat.