Abstract: The peak pressure of water hammer waves can be accurately captured by using traditional TVD schemes solving a quasi-constant friction model, but their attenuation and distortion cannot be exactly described by such models. Further studies on TVD schemes solving unsteady friction models are needed to eliminate the shortcoming of traditional models in pipeline design and management. In this work, we have developed a new numerical method for solving the one-dimensional water hammer equations based on the Sweby’s TVD scheme and Brunone’s IAB unsteady friction model and verified it through comparison with previous studies of classical water hammer experiment and application to engineering examples. It was compared with a traditional TVD scheme solving a quasi-constant friction model and the method of characteristics solving the unsteady friction model. Results show that our new method can capture the attenuation and distortion of water hammer waves in each of the calculated wave cycles and improve the accuracy in calculation of the resulting pressure peaks. And its numerical errors do not increase with simulation time, remaining less than 3% in peak pressure and no larger than 0.5 radian in phase shift for all the calculated wave cycles. With its computational cost comparable to that of traditional models, the new model is obviously superior for engineering application and research.