Ship Shoal has been a high-priority target sand resource for dredging activities to restore the eroding barrier islands in LA, USA. The Caminada and Raccoon Island pits were dredged on and near Ship Shoal, which resulted in a mixed texture environment with the redistribution of cohesive mud and noncohesive sand. However, there is very limited knowledge about the source and transport process of suspended muddy sediments near Ship Shoal. The objective of this study is to apply the Regional Ocean Modeling System (ROMS) model to quantify the sediment sources and relative contribution of fluvial sediments with the estuary and shelf sediments delivered to Ship Shoal. The model results showed that suspended mud from the Atchafalaya River can transport and bypass Ship Shoal. Only a minimal amount of suspended mud from the Atchafalaya River can be delivered to Ship Shoal in a one-year time scale. Additionally, suspended mud from the inner shelf could be transported cross Ship Shoal and generate a thin mud layer, which is also considered as the primary sediment source infilling the dredge pits near Ship Shoal. Two hurricanes and one tropical storm during the year 2017–2018 changed the direction of the sediment transport flux near Ship Shoal and contributed to the pit infilling (less than 10% for this specific period). Our model also captured that the bottom sediment concentration in the Raccoon Island pit was relatively higher than the one in Caminada in the same period. Suspended mud sediment from the river, inner shelf, and bay can bypass or transport and deposit in the Caminada pit and Raccoon Island pit, which showed that the Caminada pit and Raccoon Island pits would not be considered as a renewable borrow area for future sand dredging activities for coastal restoration.