Based on the fractional order grey accumulating generation operator and reducing generation operator, the fractional order grey prediction model is proposed. The even GM(1,1) is a special case of the fractional order grey prediction model with ?? = 1. Then the particle swarm optimization algorithm for the optimized fractional order of the minimum average relative error is presented. The case study shows that the fractional order operator GM(1,1) with optimized order can achieve better fitting precision than DGM(1,1), GM(1,1) and some other optimized GM(1,1) models.