In the context of the comprehensive advancement of the green water protection campaign, guiding river chiefs to effectively assume inter-generational responsibilities and promote the ecological sustainability of urban inland rivers is a critical practical challenge. This paper addresses the issues of "difficult inter-generational coordination of river chiefs and limited internal government supervision" within the sustainable governance framework of urban inland rivers. Utilizing evolutionary game theory, we develop a four-player evolutionary game model that includes the previous and next generations of river chiefs, government administrative supervision departments, and the public. By examining the strategic evolution of the system under various influencing factors, we explore how local government administrative supervision departments can collaborate with the public to establish an internal and external dual-layer multi-governance supervision system, thereby encouraging river chiefs to fulfill their inter-generational responsibilities. Our findings indicate that the influence between the two generations of river chiefs is asymmetric over time and space, with the governance strategy of the previous generation having a more significant impact on the next. As comprehensive management costs increase, both generations exhibit a tendency towards negative governance intentions. Reducing the cost-sharing ratio alleviates the burden on the previous generation but hinders the continuity of governance by the next, leading to interruptions in management efforts. Enhanced administrative supervision can accelerate system stabilization, significantly affecting both generations of river chiefs. However, relying solely on increased enforcement without adjusting rewards and penalties will gradually diminish its effectiveness. Changes in performance-based rewards, penalties, and base salaries affect system stability to varying degrees, but base salary adjustments have a limited impact compared to the responsiveness of performance incentives. Although increased public reporting intensity does not significantly alter the strategy choices of the two generations of river chiefs, it does contribute to reducing system stabilization time. This study not only enriches the theoretical understanding of inter-generational responsibilities of government officials and sustainable environmental governance but also provides a theoretical foundation for the sustainable ecological management of urban inland rivers. By analyzing the impact of various factors on the strategic choices of river chiefs across generations, it offers insights into the internal mechanisms of urban inland river ecological governance. Furthermore, it supports local government administrative supervision departments in collaborating with the public to build a dual-layer multi-governance supervision system, facilitating continuous improvements in the ecological environment of urban inland rivers.