The present invention relates to a process for thermal cracking of heavy petroleum oil, in which when a thermal cracking facility having a cracking furnace, two or more of trains each comprising two reaction vessels and one distillation tower is operated, each train is operated by repeating a cycle comprising drawing the heavy petroleum oil from the cracking furnace, feeding the drawn heavy petroleum oil into the first reaction vessel and then feeding the drawn heavy petroleum oil into the second reaction vessel, steam is directly brought in contact with the heavy petroleum oil to be thermally cracked, and gaseous cracked substances produced and steam are introduced into the distillation tower to be distilled and separated, wherein phase delay is provided for the cycle repeated in each train so that the thermal cracking facility is operated with the different initiation time of feeding to the first reaction vessel in each train. According to the present invention, the instability of the flow-in quantity of the gaseous substances to the distillation tower is improved, and the improvement of separation performance, the increase of processing capacity of the facility and the like can be achieved.