A one-dimensional hydraulic HEC-RAS model was developed to forecast the change in salinity in the tributaries of the Co Chien and Hau Rivers in Tra Vinh province, Vietnam. The boundary data includes river discharge at Can Tho and My Thuan, water levels, and salinity at coastal monitoring stations. Six monitoring stations along the Co Chien River and Hau River were selected to study salinity changes. Four scenarios for the period 2020–2050 were selected, including SLR17, SLR22, SLR26L, and SLR26H, corresponding to sea level rise (17, 22, and 26 cm) and upstream river discharge decrease (in the ranges of 100–128% and 80–117% at Can Tho and My Thuan, respectively) in the dry season based on new climate change scenarios in Vietnam and previous studies. The results highlight that when the average discharge at Can Tho and My Thuan reduces, the salinity increases more significantly than the impact of sea level rise. Salinity at the monitoring stations in Tra Vinh province is projected to increase within the ranges of 4–21% and 3–29% along the Co Chien River and Hau River, respectively. In addition, sea level rise is seen to affect the discharge distribution into the Co Chien River. It suggests an urgent need to raise farmers’ awareness of climate change adaptation, investment in production equipment, and appropriate regulation of riverbed mining and activities upstream in the Mekong River.