The global warming problem caused by carbon emissions has significantly influence the sustainable development of human society. Nowadays, more and more countries and regions are taking measures to cope with this problem. Researches indicated that consumers' energy consumption has a significant influence on the carbon emissions. To guide, regulate and motivate consumers' energy consumption behavior is benefit to make a low-carbon energy consumption pattern, which has an important theoretical and realistic significance. Based on the personal carbon trading scheme, we construct an energy use choice model and analyze the market equilibrium of the carbon trading. It is shown that personal carbon trading scheme can motivate consumers to choose clean energy and to make a low-carbon energy consumption pattern. The supply curve of the carbon allowance is different from the general commodity supply curve. When the carbon price increases, the supply quantity of the carbon allowance will decrease. The initial allocated carbon allowance should be set at an appropriate level, thus, the carbon trading among consumers can be achieved.