A multi-car elevator control device for controlling an operation in such a manner that a rear car can stop away from a periphery of a fire floor. The multi-car elevator control device includes a running-enabled section calculator for calculating, as a running-enabled section, a range of a floor in which a stop can be carried out to open a door without a collision with a front car which stops, a fire floor information acquiring part for acquiring fire floor information, an in-fire stop prohibition section calculator for calculating, based on the fire floor information, an in-fire stop prohibition section for prohibiting the stop of the car, and a running permission deciding part for deciding a running permission of an elevator by referring to the running-enabled section and the in-fire stop prohibition section.