In order to study flashover phenomenon of special fire in building under construction, a fire energy conservation equation was first established in this paper. Then,the critical temperature of thermal smoke during the flashover was determined by the catastrophe potential function based on the swallowtail catastrophe theory. Finally, the software FDS was adopted to simulate the fire flashover considering different construction scenarios, so that the corresponding fire characteristic parameters can be obtained. The results show that different fire combustible materials at different construction stages lead to different flashover time points. With the increase of ventilation velocity, the rate of fire heat release increases slowly, whereas the visibility of smoke increases rapidly. In addition, the fire characteristic parameters are highly related to the fire sources. Thus, flashover is more likely to occur in narrow space, leading to an obvious chimney effect, especially for the unclosed stairwell.