To overcome the problems of model error and initialized value of the existing GM(1,1) power model, the grey discrete power GM(1,1) model is constructed, and grey discrete power GM(1,1) is transformed into fractional order grey discrete power GM(1,1). An optimization model is constructed with the objective of minimum average relative error, the constraints of relationships between parameters in order to optimize the power exponent and the accumulation order, and the optimization values of accumulation order and power exponential are determined by using the quantum genetic algorithm. Finally, two application examples, named settlement volume of subgrade and chinese high technology enterprises, show that the proposed model has higher precision accuracy.