An agricultural drought disaster was analyzed with the new insight of rescaled statistics (R/S) and wavelet analysis in this study. The results showed that: (1) the Hurst index of the agricultural disaster area, the inundated area of agricultural drought disaster, and the grain loss was 0.821, 0.874, and 0.953, respectively, indicating that the process of the agricultural drought disaster had stronger positive continuity during the study period; (2) based on the Morlet analysis of the agricultural disaster area, the inundated area of the agricultural drought disaster, and the grain loss of China from 1950 to 2016, the time series of the agricultural drought had multiple time scale features with the periodic variation on a large scale containing the periodic variation on a small scale; and (3) in the last 67 years, the strong wavelet energy spectrum of the agricultural disaster area, the inundated area of the agricultural drought disaster, and the grain loss was at the time scale of ≈22–32 years, ≈24–32 years, and ≈25–32 years, respectively. In addition, the first major period in the agricultural drought disaster area, the inundated area of agricultural drought disaster, and the grain loss had average periods of approximately 16 years, 16 years, and 18 years, respectively.