To more accurately identify and predict drought events, this study uses the long series of daily runoff in the Linjiacun Hydrological Station from 1960 to 2020 as data input. By combining statistics and dynamics methods, we calculated hydrological drought probability P, runoff fractal dimension D2 and runoff Lyapunov exponent LE, and established functional relationships for P-D2, P-LE to solve the drought probability from the perspective of chaotic dynamics. Furthermore, the runoff Z-index sequence is used to reconstruct the phase space, within which the future drought events are predicted. The research results show that the statistical parameter P has a good linear relationship with the chaotic parameter D2 and LE, with regression equation R2 values of 0.93 and 0.83, respectively. Within the prediction interval, the runoff Z-index for 2021 is predicted to be 1.69 by the chaotic prediction model, corresponding to a hydrological drought state of “no drought”. This conclusion is consistent with the actual hydrological situation, demonstrating a good predictive performance of the model. This research can provide a new approach for the study of drought theory.