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The global community and the academic world have paid great attention to whether and when China's carbon dioxide (CO2) emissions will peak. Our study investigates the issue with the Nonlinear Auto Regressive model with exogenous inputs (NARX), a dynamic nonlinear artificial neural network that has not been applied previously to this question. The key advance over previous models is the inclusion of feedback mechanisms such as the influence of past CO2 emissions on current emissions. The results forecast that the peak of China's CO2 emissions will occur in 2029, 2031 or 2035 at the level of 10.08, 10.78 and 11.63 billion tonnes under low-growth, benchmark moderate-growth, and high-growth scenarios. Based on the methodology of the mean impact value (MIV), we differentiate and rank the importance of the influence factors on CO2 emissions whereas previous studies included but did not rank factors. We suggest that China should choose the moderate growth development road and achieve its peak target in 2031, focusing on reducing CO2 emissions as a percent of GDP, less carbon-intensive industrialization, and choosing technologies that reduce CO2 emissions from coal or increasing the use of less carbon-intensive fuels.