The Accelerator Driven Advanced Nuclear Energy System (ADANES) is currently undergoing research and development (R&D), presenting challenges in cost estimation due to significant uncertainties. Traditional nuclear power cost assessment methods, tailored for mature technologies, lack relevance for advanced systems like ADANES. To address this gap, our study proposes a unique cost analysis approach, dividing ADANES into two stages: the experimental research and development (ERD) stage and the industrial demonstration (ID) stage. Specificlly, in the ERD stage, this study employs a Logistic function-based evaluation method that considers factors such as construction period extension, the proportion of fixed costs, and the upper limit of cost estimated by experts to address potential cost overruns. For the ID stage, this study utilizes a stochastic differential equation (SDE) to account for uncertainties. Monte Carlo simulation is employed to analyze the impact of parameter changes, including construction period extension and acceptable upper limits of cost and duration. Results reveal a substantial increase in expected cost during the ERD stage, ranging from 100% to 140% of the original budget when extending the experimental research duration by 10% to 50%. The ID stage demonstrates an even more significant impact, with a 50% construction period extension resulting in an expected cost of 182% of the original budget. The study suggests that judiciously extending acceptable cost and duration caps can enhance the project's success rate. This innovative cost analysis approach provides valuable insights for navigating the uncertainties associated with ADANES development. •A cost analysis approach is introduced for the disruptive ADANES nuclear energy system.•It employs a logistic function-based evaluation method and stochastic differential equation to account for uncertainties.•A case study validates the method, revealing the numerical relationship between time extension and cost overrun of ADANES.