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Introducing carbon trading is an essential way to decarbonize the power system. Many existing studies mainly consider source-side unilateral carbon trading (UCT). However, there are still rare studies considering source-load bilateral carbon trading (BCT). The effect of source-load BCT on system-wide carbon mitigation is worth studying. To fill this research gap, a hierarchical low-carbon economic-dispatch model with source-load BCT based on the Aumann–Shapley method was proposed. In the first layer, economic-dispatch was conducted to minimize the power-generation costs and source-side carbon-trading costs. Then, based on the carbon-emission flow (CEF) theory, the actual load carbon emissions can be obtained and passed to the second layer. At the second layer, the demand-response optimization was performed to minimize the load-side carbon-trading costs. Finally, the proposed model was tested on the modified New England 39-bus and IEEE 118-bus systems using the MATLAB/YALMIP platform with the Gurobi solver. The results indicate that the proposed model can effectively facilitate peak-load shifting, wind-power consumption, and carbon mitigation. Furthermore, compared with the models only considering source-side or load-side UCT, the proposed source-load BCT model has obvious advantages in carbon mitigation. [ABSTRACT FROM AUTHOR]