An elevator group control apparatus which controls an elevator system where an upper car and a lower car serve in a same shaft and are allowed to go up and down therein independently and where a plurality of shafts are comprised, comprising: a destination floor registration device to register a destination floor, installed at each hall where the upper car or the lower car may stop; car travel range calculating means which provisionally assigns a destination call registered by the destination floor registration device to each car and calculates the travel range of a car to which the destination call is provisionally assigned and the travel range of the other car in the shaft where the provisionally assigned car serves; assignment candidate selecting means which, based on the bottom of the travel range of the upper car calculated by the car travel range calculating means and the top of the travel range of the lower car calculated by the car travel range calculating means, selects the provisionally assigned car as a candidate for assignment to the destination call in the case collision is avoided and excludes the provisionally assigned car from a candidate for assignment to the destination call in the case collision may occur; evaluation index calculating means to calculate an evaluation value only for each of the cars selected as candidates for assignment to the destination call by the assignment candidate selecting means; assigning means to finally determine which of the candidates is to be assigned to the destination call based on the result of calculation by the evaluation index calculating means; and operation control means to control the operation of the assigned car based on the destination call. a destination floor registration device to register a destination floor, installed at each hall where the upper car or the lower car may stop; car travel range calculating means which provisionally assigns a destination call registered by the destination floor registration device to each car and calculates the travel range of a car to which the destination call is provisionally assigned and the travel range of the other car in the shaft where the provisionally assigned car serves; assignment candidate selecting means which, based on the bottom of the travel range of the upper car calculated by the car travel range calculating means and the top of the travel range of the lower car calculated by the car travel range calculating means, selects the provisionally assigned car as a candidate for assignment to the destination call in the case collision is avoided and excludes the provisionally assigned car from a candidate for assignment to the destination call in the case collision may occur; evaluation index calculating means to calculate an evaluation value only for each of the cars selected as candidates for assignment to the destination call by the assignment candidate selecting means; assigning means to finally determine which of the candidates is to be assigned to the destination call based on the result of calculation by the evaluation index calculating means; and operation control means to control the operation of the assigned car based on the destination call.