A numerical model is developed for the prediction of transient water quality in an estuary represented as a network of branched and looped, one-dimensional channels. The time scale of the model is of the order of minutes and is called tidal time. Four constituents, salinity, temperature, bio-chemical oxygen demand (BOD), and dissolved oxygen (DO), are included in the mathematical model. In solving the conservation of mass equations for the various water quality constituents, tidal time permits formulation of an ocean boundary condition related to the direction of tidal flow. The numerical solution procedures used in the study are based on the method of weighted residuals, which is an application technique of the finite element method. To demonstrate the predictive capability of the mathematical model, computed results are compared with available data from dye test experiments.