PURPOSE: To increase the energy efficiency in the preparation of the titled compound by the ammoxidation reaction of an olefin, by utilizing the relatively low- temperature sensible heat or latent heat generated in the reaction system and wasted so far, as a cooling source or a heating source.

CONSTITUTION: The ammoxidation reaction product of an olefin is quenched with water in a quenching tower 3, and absorbed in absorbing water in the absorption tower 8. The absorbing liquid is subjected to the extractive distillation with water solvent in the recovery tower 13, and the distillate from the top of the tower is sent successively to the hydrogen cyanide-removal tower 21, the dehydration tower 25 and the product tower 28, etc., and the unsaturated nitrile is separated by distillation. In the above process, the absorbing liquid discharged e.g. from the absorption tower 8 is heated, before the preheating with the solvent water in the heat exchanger 12, with the circulating water heated by passing through the circulation water cooling liquid 6 in the quenching tower 3. As an alternative method, the hot water solvent discharged from the line 15 of the recovery tower 13 is used as the heat source of the reboiler 29 of the product tower 28 (or the reboilers 22, 26 of the towers 21, 25), and then passed through the heat exchanger 12 to preheat the absorbing liquid.