In this study, a mathematical framework was developed for the sustainability prioritization of alternative low-carbon ammonia production routes. In the framework, a four-dimensional assessment system that can incorporate both quantitative and qualitative criteria from the environmental, economic, social-political, and technical concerns was firstly established. Subsequently, a hybrid Entropy-FANP method was employed to determine the criteria's weight by combining the objective data and subjective opinions; a novel PRSRV approach was developed to rigorously rank the alternative routes by aggregating the absolute sustainability performance and relative sustainability balance of each alternative. The proposed framework was applied to prioritize five promising low-carbon routes for ammonia production, i.e. wind turbine electrolysis (WGEA), solar photovoltaic electrolysis (PVEA), hydropower electrolysis (HPEA), biomass gasification electrolysis (BGEA), and nuclear high temperature electrolysis (NTEA), yielding the sustainability ranking of HPEA > BGEA > WGEA > PVEA > NTEA. The robustness and effectiveness of the proposed framework were verified by conducting the sensitivity analysis and comparing the results determined by the proposed framework with those determined using the previous approaches.