In order to reveal the response relationship between meteorological drought and hydrological drought characteristic variables in upper reaches of the Hanjiang River Basin, the standardized precipitation index and standardized runoff index were chosen to reflect the meteorological drought and hydrological drought, respectively, and the linear and nonlinear function models were used to construct the meteorological-hydrological drought characteristic variable response probabilistic model. Then, meteorological-hydrological drought characteristic variable probability curves were established based on the Copula function coupled with the Bayesian network probabilistic model. The results show that the optimal response models of meteorological-hydrological drought duration and intensity are the linear function model and the Gumbel Copula function-based nonlinear model, respectively; the optimal joint distribution functions of drought duration and intensity are the Frank Copula function and Gumbel Copula function, respectively; the response probability of hydrological drought duration and intensity increases with the meteorological drought characteristic variables, and the rate of change of response probability of hydrological drought decreases gradually, and finally tends to level off, and the rate of change of response probability of hydrological drought intensity is low.