The hydraulic-mechanical-electrical coupling dynamics of hydropower plants during transient processes is a key issue in engineering practice. Numerical simulation of transient process could provide support for practical operation of hydropower plants and avoid dangerous working conditions, indirectly increasing the unit operation time and improving economic benefits. Numerous previous studies used the transfer function method (TFM) for modelling and simulation of hydropower plants, but many previous models are oversimplified and cannot simulate some complicated transient processes. To solve this problem, a nonlinear and flexible model of hydropower plant is developed on Simulink in this work. TFM is adopted to model the waterway system with complicated hydraulic components, and an improved scheme of TFM is recommended. Quantitative comparison of time-domain and frequency-domain simulations demonstrates the accuracy of the improved TFM in simulating the water hammer in the waterway system. Besides, the improved TFM is applied to combine with complicated electrical modules on Simulink, simulating hydraulic-mechanical-electrical coupling dynamics under hydraulic disturbance and three-phase fault. In conclusion, the method developed in this paper has advantages of accuracy, flexibility, and expansibility, enabling deeper understanding and refined simulation for transient processes of hydropower plants. The hydraulic-mechanical-electrical coupling model can be used to simulate a variety of working conditions in engineering practice and support future research on the dynamic characteristics of hydropower plants.