Low-carbon development has been widely regarded as a key strategy for tackling the challenges posed by climate change. Measuring low-carbon performance can provide policy makers valuable information for monitoring the progress of low-carbon development in an economy such as a city. Composite indicator, owing to its transparency and ease of communication to the public, has been touted as a useful analytical tool for measuring low-carbon performance. The construction of composite indicators often takes the compensability assumption which allows the full substitutability between underlying indicators. In this paper, we argue that the compensability assumption needs to be restricted in assessing low-carbon performance. A non-compensatory approach based on the outranking relation is used to construct composite low-carbon performance indicator. A more efficient heuristic procedure is proposed to handle the computational complexity in deriving the final comprehensive rankings. The approach has been applied to assess the city-level low-carbon performance in China. A sensitivity analysis is conducted to investigate the impacts of various parameters on the modeling results.