As a renewable energy technology, agricultural waste power generation holds considerable potential for substituting coal-based power and mitigating carbon emissions. Nevertheless, the stability and sustainable development of its supply chain encounter significant challenges. To systematically examine the key influencing factors and their interrelationships, this study employs the PESTEL framework to identify 21 critical factors across six dimensions—political, economic, social, technological, environmental, and legal—and constructs a fuzzy cognitive map (FCM) model to enable dynamic system reasoning and evolutionary analysis. The findings reveal that the cost of agricultural waste power generation, supply accessibility, availability of financial market instruments, policy support, and societal awareness of corporate responsibility are the core drivers shaping the system’s development. Notably, economic cost exhibits the highest sensitivity in the model, exerting the most pronounced influence on system stability, while political factors serve as a strong external catalyst. Furthermore, five major barriers to development are identified: cost pressures, logistical and supply chain inefficiencies, capital shortages, inadequate coordination mechanisms, and insufficient alignment of stakeholder interests. To address these challenges, this study recommends strengthening cost subsidies and establishing robust collection and storage infrastructure in the short term; in the medium to long term, it advocates enhancing industrial policy frameworks, developing digitalized coordination platforms, and instituting benefit-sharing mechanisms to foster multi-stakeholder collaboration—ultimately advancing the efficiency, resilience, and sustainability of the agricultural waste power generation supply chain.