Furfural is produced by mixing an aqueous feedstock solution containing C5 sugar and/or C6 sugar with a heated high boiling, water-miscible solvent, such as sulfolane, and a solid acid catalyst. Furfural product and water can be distilled off, leaving non-volatile solvent behind. Furfural yields of over 70% at as high as 99% conversion have been obtained with this process with sulfolane as the reaction solvent and zeolite beta as the solid acid catalyst. Also, certain by-products (e.g., humins) solubilized in the reaction solvent can be precipitated by addition of water or aqueous feedstock solution and then removed by filtration, thereby providing a convenient and effective way of removing these undesirable byproducts from the reaction mixture.