Hydrologic characteristics including extreme-flow events in many rivers around the world have been altered due to the climate change and human activities. Most available research concerns about the extreme event trend, frequency and duration in a single river rather than the synchronicity or coincidence probability among different tributaries. Accurately knowing the coincidence probability of hydrologic extreme-flow events is vital for better water resources allocation and project design. Joint distribution constructed by the copulas function is a widely used method to conduct this issue. However, studies conducted by the copulas function are mostly carried out in a bivariate environment and ignore the nonstationary. These may not comprehensively reflect the hydrologic characteristics under the changing environment. This paper analyzes the related hydrologic low-flow changes considering the nonstationary under the changing environment in the Wei River Basin, China, where the climate tends to be drier. These analyses are obtained by using trivariate copulas function and Kendall’s return period method to derive the joint distribution of hydrologic low-flow in a seasonal time scale. The results mainly show that the coincidence probabilities of low-flow among three tributaries of the Wei River in four seasons after the change point are basically higher than those before the change point. It may indicate that the low-flow negative impacts in the whole Wei River Basin in four seasons may be intensified (which needs to be paid more attention) under the changing environment.