Herein, we disclosed a method of preparing a nanocatalyst containing nickel-cobalt by impregnation in a hydrochloric acid medium. Optimal conditions were established for all stages of nanocatalyst preparation using the method of probabilistic–deterministic experiment planning: hydrochloric acid concentration—1 mol/L, ratio of HCl concentration to nickel concentration—20, ratio of HCl concentration to cobalt concentration—20. The method of planning the experiment of preparing a nanocatalyst allows varying all the factors simultaneously and obtaining quantitative estimates of the main effects and effects of interaction, as well as establishing the dominant factors affecting the activity and selectivity of the nanocatalyst during the hydrogenation of benzothiophene. The multifactorial equation was obtained, which allowed us to calculate the optimal manufacturing parameters of the nanocatalyst, providing high activity and selectivity during the hydrogenation of benzothiophene. In the proposed nanocatalyst, a readily available natural chrysotile–asbestos with a nanotube diameter of 60–75 nm was used as a carrier for the benzothiophene hydrogenation process.