The modification effect of NiCu–SiO2 catalysts by molybdenum on their activity and selectivity in the hydrogenation of furfural—a product of the acid hydrolysis of hemicellulose biomass—was studied. The original NiCu catalyst was synthesized by the sol–gel method and stabilized with 10 wt % SiO2 by impregnating the calcined sol–gel with an appropriate amount of ethyl silicate. Molybdenum was introduced by impregnation of the original catalyst with an aqueous solution of ammonium molybdate. The selective hydrogenation of furfural was carried out in a batch reactor at temperatures of 100–200°C and a hydrogen pressure of 6 MPa. It was shown that an increase in the process temperature in the presence of the molybdenum-containing catalyst increases the yield of 2-methylfuran and products of complete hydrogenation. At low process temperatures a small amount of 2-methylfuran is formed; the main products are furfuryl and tetrahydrofurfuryl alcohols. The modified NiCuMo–SiO2 catalysts exhibit higher activity in hydrogenation of furfural and greater 2-methylfuran selectivity than the respective parameters of NiCu systems, due apparently to the formation of NiMo(Cu) solid solutions, and the formation of Mox+ on the catalyst surface.