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Performance appraisal is a key link in the performance payment mechanism of government-paid Public-Private Partnership (PPP) projects. As the performance appraisal of PPP projects is highly professional and complex, it is usually necessary to introduce a third-party performance appraisal institution to evaluate the project outputs of the private investor. However, driven by economic rent, the private investor has the incentive to seek rent from the third party in the performance appraisal process, leading to the low overall performance level of PPP projects and the inability to achieve the PPP performance appraisal goal effectively. To explore how to avoid rent-seeking in performance appraisal and improve the overall performance of government-paid PPP projects, a tripartite evolutionary game model between the behaviour, third party, and the public sector has been constructed. Based on the evolutionary game model, this study analyses the evolutionary stability of each player's strategy, discusses the influence of various factors on the strategy selection of the three-party, and further analyses the stability of the equilibrium point of the three-party game system. The findings reveal that the public sector can slow down the rent-seeking behaviour of the private sector by setting up a reasonable reward and punishment mechanism. The design of a reasonable reward and punishment mechanism must meet the following conditions: (1) the sum of the reward and punishment of all parties is greater than the speculative income; (2) the amount of performance fee withheld for the private investor is greater than the difference between the project operating cost saved and the speculation cost. The research provides technical support for the design of the performance appraisal mechanism of government-paid PPP projects.