Time-varying moments models based on Pearson Type III and normal distributions respectively are built under the generalized additive model in location, scale and shape (GAMLSS) framework to analyze the nonstationarity of the annual runoff series of the Weihe River, the largest tributary of the Yellow River. The detection of nonstationarities in hydrological time series (annual runoff, precipitation and temperature) from 1960 to 2009 is carried out using a GAMLSS model, and then the covariate analysis for the annual runoff series is implemented with GAMLSS. Finally, the attribution of each covariate to the nonstationarity of annual runoff is analyzed quantitatively. The results demonstrate that (1) obvious change-points exist in all three hydrological series, (2) precipitation, temperature and irrigated area are all significant covariates of the annual runoff series, and (3) temperature increase plays the main role in leading to the reduction of the annual runoff series in the study basin, followed by the decrease of precipitation and the increase of irrigated area.