Time series characterized by periodic fluctuations are widespread in reality behavioural systems, and accurate forecasting of them has important practical application value. In this paper, based on the idea of discrete grey model, dual interaction effects and the nonlinear characteristics of the system are considered under the perspective of dual processing, and the fluctuating trend of the periodic sequence is portrayed through the introduction of the periodic dummy variable, and at the same time, combined with the extended periodic rolling time window method, the rolling discrete grey periodic power model with the interaction effect under dual processing is proposed, namely DIE-RDGM(1,1,T)α model. Differential evolution algorithm (DE) are employed to determine the optimum power index. Finally, the new model was compared with nine other forecasting models by three instances and applied to the problem of agricultural drought forecasting in Zhoukou City and Anyang City, Henan Province. The results show: (1) The new model has demonstrated strong competitiveness, confirming its rationality, validity, and superiority. (2) The DE is suitable for power index optimization search. (3) The new model can better describe the periodic change rule of seasonal-scale soil moisture in the two cities, and the forecast results are consistent with the actual drought conditions.