The allocation mechanism of carbon abatement quotas is an important regulation to abate carbon emissions. Data envelopment analysis (DEA) is adopted in this study to measure the allocation among industrial firms. Different from previous studies, our research takes the carbon abatement capability (CAC) as one crucial focus. A DEA model is developed to measure the CAC by using slacks. A novel centralized allocation model incorporating the slacks-based target is proposed, with both DEA-determined and user-determined settings of carbon abatement bounds. We further propose two scenarios to represent the utilization possibilities of CAC in allocation, and they are CAC-minimum and maximum scenarios. The CAC-minimum scenario is defined as making full use of the CAC in allocation, while the CAC- maximum scenario focuses on reserving the most CAC for the future. Both mechanisms are applied to an application of 499 Chinese industrial firms to determine the effectiveness. By measuring the allocation results between the two scenarios, the consideration of CAC is proved to affect the allocation significantly. Comparisons in allocation results between scenarios and between different firm groups are also investigated. Firms in CAC-minimum scenario will make full use of current CAC to achieve the allocation. Such allocation would result in less economic loss and require minimal technological progress. Firms in CAC-maximum scenario are more environmental-friendly and aim to achieve the most carbon abatement possible. This allocation scenario should be advocated to enhance the firm's future competitiveness. Both scenarios are analyzed in the research to design a balanced allocation.