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The household energy management system (HEMS) has become an important system for energy conservation and emission reduction. In this study, home energy management considering carbon quota has been established. Firstly, the household photovoltaic output model, load model of various electrical appliances, battery load model, and charging and discharging of electric vehicles (EVs) model are established. Secondly, the carbon emission and carbon quota of household appliances and EVs are considered in these models. Thirdly, the energy optimization model of minimum the household user’s total comprehensive operation cost with the minimum total electricity consumption, carbon trading cost, battery degradation cost, and carbon quota income are proposed, taking into account constraints such as the comfort of users’ energy use time. Subsequently, the improved particle swarm optimization (IPSO) algorithm is used to tackle the problem. Compared to the standard particle swarm optimization (PSO), the IPSO has significantly improved the optimization effect. By comparing the optimization results in different scenarios, the effectiveness of the strategy is verified, and the influence of different carbon trading prices on optimal energy scheduling has been analyzed. The result shows that the comprehensive consideration of carbon trading cost and total electricity cost can reduce the household carbon emissions and the total electricity cost of the household user. By increasing the carbon trading price, the user’s carbon trading income and the EV carbon quota income increase, and the overall operating cost decreases; the guidance and regulation of carbon trading price can make a valuable contribution to HEMS optimization. Compared to the original situation, the household carbon emissions are reduced by 14.58 kg, a decrease of over 21.47%, while the total comprehensive operation cost are reduced by 14.12%. Carbon quota trading can guide household users to use electricity reasonably, reducing household carbon emissions and the total cost of household electricity.