In this paper, a two-dimensional numerical calculation algorithm for water-quality modeling is presented. The algorithm is designed specifically for river systems with complicated geometric conditions. When velocity field data of the river are not available, the numerical calculation algorithm for the water-quality modeling can be used to project river-water quality by using a topographic map of the river course and a finite element method. The calculation results of the water-quality model can show the concentration fields of various pollutants. The water-quality model was applied to a case-study in the Hengyang City section of Xiangjiang River in Hunan Province, China. The river under consideration is winding and has an isle between two branches. In 1995, Chinese government secured a World Bank loan to conduct a Waterways Project in the study region. It was expected that construction works in the river section might affect water quality. Given that the project would change the hydrological regime of the river system and discharges, and so would affect water quality, there would be a need for model results that would predict the water-quality impacts of the Waterways Project. In particular, the study intended to apply the model to identify changes in river-water quality associated with the construction of Dayuandu navigation key project. It is hoped that the numerical calculation algorithm for the water-quality modeling presented in this paper can also be applied to other shallow rivers with similar topographical conditions.