A method relating to oil refining, which can be used to produce low-sulfur diesel fuel, comprising oil demineralization and distillation, and extraction and mixing of diesel fractions, followed by hydrogen refining of the mixture. In an atmospheric tower, two diesel fractions that boil at 171-341° C. and 199-360° C. are extracted. The 199-360° C. fraction is sent for liquid extraction to purify it from benzalkylthiophens. Amide, a product of organic amine interaction with organic acid, is used as the extractant. Fractions are then mixed, maintaining the balance ratio (based on the output) of 171-341° C. and 199-360 ° C. after refining. When refined using the ASTM D-86 method, the mixture of these fractions has an end boiling point no higher than 360° C. The technical result is production of diesel fuel with a 171-360° C. fractional composition and sulfur content of no higher than 10 ppm.