Hydrological forecasting can provide the basis for dealing with the conflict between flood control and water use. This paper proposes a flood and sediment forecasting method for rivers by deriving an energy equation which describes the conservation of potential slope, kinetic slope, and friction slope of a river reach. The equation contains an additional term, the rate of change of stage, which has a significant effect on the propagation of flood waves, as compared with the Saint-Venant momentum equation. The energy equation has been found to provide more accurate results in the hydraulic calculation of the Han River, China, than the Saint-Venant momentum equation. Based on this energy equation, an improved diffusive model (IDM) was derived. By modelling the flood process for the Yellow River, China, the IDM was compared with the classical diffusive model (CDM) showing that the IDM gives better results. The time series form of IDM with time-variant parameters was used for real-time flood and sediment forecasting of the Yellow River. The recursive ordinary least-squares (ROLS) approach, improved by introducing an effective matrix, was used for on-line identification of parameters.