A significant inability of the existing river flood routing models is their limitations to simulate single variable (discharge or water stage). The research proposes a "general bivariate" coupling routing method that improves the universality of Muskingum method and can simulate double variables simultaneously. The proposed model is based on the flow continuity equation and two different forms of river reach storage equation: (1) the storage of a river channel equals the product of the mean cross-sectional area and the river channel length; (2) the storage of a river channel equals the product of the mean discharge of a river channel and the flow travel time. In order to consider the representative of diverse factors, including geographical scope, river channel features, flood magnitude, hydraulic characteristics and et al, the proposed model is tested by observed data of flood seasons which is selected form 16 rivers channels of 4 river basins in China. The rationality of model structure and performance of model simulations are determined comprehensively. When compared with Muskingum routing method, the approach can lead to more accurate simulations and the performance is more stable than Muskingum routing method. The proposed model is more versatile than Muskingum model in real cases.