Simulating suspended sediment discharge in large river systems has been challenging, particularly regarding effective parameterization and accounting for the damming effects over the regional (or river basin) scale. To overcome these two challenges, we developed a suspended sediment module on top of the Model for Scale Adaptive River Transport (MOSART), the riverine component of the Energy Exascale Earth System Model, denoted as MOSART-sediment. MOSART-sediment takes lateral water and sediment fluxes as inputs from the land component of E3SM and represents riverine sediment transport, erosion, and deposition processes. To address the first challenge, we compiled over 2500 in-situ D50 observations from the U.S. rivers, developed a predictive model of the median sediment particle size (D50) using artificial intelligence techniques, and derived a continuous D50 map over the contiguous U.S. To address the second challenge, we leveraged the existing reservoir module in MOSART to account for two major damming effects on suspended sediment transport: 1) reservoirs directly trap suspended sediment before the dams; 2) reservoirs modify hydraulic conditions for sediment transport via regulating streamflow. Besides D50, all other model parameters were also estimated a priori without calibration. We applied MOSART-sediment to the contiguous United States, successfully validated it against historical observations of monthly streamflow and sediment discharges at 35 river gauges, and showed that suspended sediment discharge in managed rivers is affected more by reservoirs' direct trapping of sediment particles than by their flow regulation. This new sediment model has at least two important implications: 1) it enables future modeling of the transportation and transformation of carbon and nutrients carried by the fine sediment along the river-ocean continuum to close the global carbon and nutrients cycles; 2) it can be used as a tool to improve process-based understanding of Earth-human system interactions around large, complex river systems.