River networks are important vehicles for water systems to maintain ecosystem health and sustainability. Especially, in plain areas with dense river networks, the river network pattern, the function of hydrological regulation and storage, as well as its complex influence mechanisms, are of great significance to the regional sustainable development. Taking the southern flood district of Kunshan City, as an example, five river network indexes at polder embankment units were introduced and analyzed in 2018: the water ratio, the river network density, the structural connectivity γ index, the river storage capacity per unit area, and the river retention capacity per unit area, to evaluate the river network structure and storage function. The Bayesian Belief Network model (BBN), a methodology based on casual-effect relationships, was applied to explore the influence mechanisms of the river network structure and function, by comprehensively considering social-ecological variables, such as land use cover, environment condition, hydraulic engineering construction, as well as policy governance and planning. The results showed: (1) The river network structure has significant spatial heterogeneity. The northern polder area is mostly lower than that in the central and southern regions, the river density in the central and western polder areas was significantly lower than the average level; besides, overall structure connectivity is moderate as compared to middle-low reach of Yangtze River plain, with relatively low value in urbanized polder embankments. (2) The difference in the storage function of river network is closely related to its structural characteristics. There are several polder embankments in the southwest and central study area that displayed complex morphological structure, and their river storage capacities per unit area is correspondingly high, showing a strong flood regulation and storage function. (3) The structural characteristics of river network can significantly affect the flood regulation function in polder embankments, and the influence degree of social-ecological factors on the river storage and retention capacity was decreased by policy, engineering, land use, and environment conditions, accordingly. (4) Based on sensitivity analysis and diagnostic analysis of the BBN model, the key state subset of key variables can be identified, which can guide the river network governance and optimization of polder embankments from the perspective of socio-ecological synergies. The results of this study can provide a theoretical support and decision-making basis for the healthy and sustainable development of river network in plain polder embankment areas and the improvement of nature-based flood control and storage functions.