The environmental issue has attracted ever-increasing attention from governments and academics in recent years. Environmental performance analysis is widely considered a crucial and useful tool for effectively protecting the environment and developing a sustainable society. Many analytical techniques have been used to assess carbon emission performance, among which data envelopment analysis (DEA) is prominent. However, few previous DEA-related carbon emission performance studies recognize that the total amount of carbon dioxide emissions is limited to a specific level by authorities; ignoring this fixed-sum requirement may lead to distortions and deviations in empirical results. This paper proposes an alternative Malmquist DEA approach for evaluating the carbon emission performance while considering fixed-sum undesirable outputs. For this purpose, we develop a generalized equilibrium efficient frontier DEA model with fixed-sum undesirable outputs and combine the model with the Malmquist productivity index (MPI). The proposed approach is applied to assess the carbon emission performance of 30 provincial regions in China from 2009 to 2015. Then we provide analytical results and policy suggestions regarding the provincial carbon emission performance in China.