This paper proposes a sequential meta-frontier Luenberger productivity index (SMLPI) that incorporates undesirable outputs to measure carbon productivity growth over time. This new index combines the concepts of sequential production technology, meta-frontier directional distance function, and the Luenberger productivity Index to produce a composite indicator, so that it can take group heterogeneities and the progressive nature of technology into consideration for productivity measurement. The SMLPI is then applied to a unique dataset of China's coal-fired power plants, including 5048 observations covering the period 1999-2008. The results show an increasing trend of carbon productivity growth during the sample period for both state- and non-state-owned power plants. Further decomposition analyses show that the production technology also exhibits an increasing trend for both groups, but the efficiency change exhibits a decreasing trend. For the state-owned group, the technology gap decreased before 2003, but increased thereafter. On the contrary, for the non-state-owned power plants, the technology gap increased before 2003, but decreased thereafter.