Ageing has adverse effects on the hydraulic-mechanical characteristics of hydropower systems (HPSs). It leads to parameter uncertainty both in the hydropower generating units (HGUs) and pipeline systems, further resulting in more severe transient conditions. Existing studies on transient state prediction of HPSs mostly do not consider the parameter uncertainty caused by HPS ageing, especially in the hydro-turbine model. This omission significantly reduces the accuracy. Therefore, a novel framework is proposed to achieve a high-precision transient state prediction of ageing HPSs. The framework includes: a refined HPS model to consider the uncertain ageing of HPSs through its uncertain parameters; a two-stage parameter identification strategy to enhance the prediction accuracy iteratively; and a parameter impact analysis which quantifies the contribution of identifying parameters to the precision improvement. Note that a comprehensive hydro-turbine model with six uncertain parameters is proposed to account for both the hydraulic-mechanical characteristic and uncertain ageing, and a fuzzy analytic hierarchy process is applied to quantify the precision. Comparative studies with on-site measurement show that: (1) The proposed framework demonstrates a 13.24% improvement in prediction performance compared to existing methods; (2) The parameters associated with HGU (especially those related to the hydro-turbine model) contribute significantly more to prediction precision, surpassing those related to the pipeline by an average factor of 9.27; (3) The contribution ranking of HGU parameters to the precision improvement is GD2> kf> μQ0>kyd>kq >kn >ηc. Overall, this study effectively improves the transient state prediction for ageing HPSs considering the uncertain parameters related to HGU and pipeline systems.