This paper attempts to explore the realizability of China's “13th Five-Year plan” objective for energy-saving and emission-reducing (ESER). Based on the internal logic relationship between new energy, carbon emissions, economic growth and carbon trading (NCEC), the 4D NCEC (acronyms) system is constructed with the aid of nonlinear dynamics theory. And then, the NCEC system for China is given after parameter acquisition. Taking energy intensity and the proportion of new energy as the measure indexes, a scenario study is carried out. The scenario analysis results show that, the target of decreasing energy intensity can be easily met with various constraints. While the objective of increasing the proportion of new energy is hard to achieve, and this objective depends on some thresholds. Only the certain speed of new energy can guarantee the increasing of new energy proportion, and the certain speed was found. The implementation of carbon trading can promote the process of ESER and realize the objectives during the “13th Five-Year plan”. However, it's not the faster carbon trading speed, the better. The appropriate speed interval is narrow. The driving function of carbon trading can help new energy to work better in ESER system.