The invention belongs to the field of chemical technology, and in particular relates to a catalyst for preparing 1, 4-butanediol or tetrahydrofuran by selective hydrogenation of dimethyl maleate and a preparation method thereof. The catalyst consists of Cu, Zn, Al, M and O, and the mol content of each metal element is as follows: 30 to 60 percent of Cu, 10 to 50 percent of Zn, 5 to 20 percent of Al and 0 to 10 percent of M, wherein M is any one of Mn, Mg and Cr. The preparation method for the catalyst comprises precipitation, ageing, washing, drying and baking of a catalyst precursor, and reduction activation before use. The catalyst is applied to the hydrogenation reaction of the dimethyl maleate, and the yield of the 1, 4-butanediol at a reaction temperature of 180 DEG C is 73.6 percent; and the yield of the tetrahydrofuran is 96 percent at a reaction temperature of 220 DEG C. Product composition of the catalyst can be well adjusted by changing the reaction condition to adapt to different market demands, and the catalyst has extremely high industrial application value.