Abstract: Aiming at the problem of modeling small sample systems with time-delay cumulative effects, this paper introduces a time-delay coefficient control term and a fractional cumulative generation operator. The paper also proposes a fractional accumulative time-delay GM (1,N) grey prediction model, using particle swarm optimization algorithm to determine the optimal time-lag effect control coefficient 𝜆 and the optimal fractional order r. Finally, combining the GDP, Fixed Asset Investment and General Public Budget Expenditure of Jiangsu province from 2013 to 2020 to establish a forecast model, and comparing the prediction results of the GM (1,1) and GM(1,N) model shows that The Fractional Accumulative Time-delay GM(1,N) model (FATGM(1,N)) can better solve the small sample multivariate with cumulative timedelay characteristics system prediction problem.