In a low-carbon power system, the demand side gradually participates in power system scheduling, providing new approaches for reducing carbon emissions. This paper proposes a two-stage low-carbon optimal scheduling model for power systems considering carbon emission flow theory and demand response based on carbon prices. First, power system economic dispatch is proposed as the first-stage model. Secondly, based on the Shapley value carbon responsibility sharing method, a calculation method for the reasonable range of carbon responsibility of each load bus is proposed. A method of formulating the step-wise carbon prices is proposed, and then the distribution of demand side carbon emissions and the carbon emission cost based on carbon emission flow theory are calculated. The demand response low-carbon scheduling is proposed as the second-stage model, using the demand side adjustment capability to reduce the carbon emissions. Finally, based on the modified PJM-5 bus system, a case study is performed on the scenario of all thermal power plants and the scenario with a wind power plant, and the carbon emissions and their costs in the system in different scenarios through simulation examples are analyzed. At the same time, it is tested in the IEEE-118 bus system, and the results verify that the model proposed reasonably calculates the carbon emission responsibility, effectively reduces the carbon emission of the system, and verifies the rationality and feasibility of the proposed model. This work is supported by the National Key Research and Development Program of China (No. 2017YFB0903402).