Global warming due to greenhouse gases (such as CO_2) emissions posts serious challenges to the sustainable development of the human society. Based on the reference method provided by the Intergovernmental Panel on Climate Change, this study calculated the CO_2 emissions of energy consumption in 30 provinces of China (excluding Tibet) from 1995 to 2014. Using exploratory spatial data analysis (ESDA), LISA time path, spatiotemporal transitions, and standard deviation ellipse analysis methods, the authors analyzed the spatiotemporal dynamics of carbon emissions of energy consumption. The results show that: (1) there was a significant positive spatial correlation of carbon emissions of energy consumption in China's provinces during 1995-2014. The inter-provincial carbon emissions differences first decreased then increased; (2) by means of LISA time path analysis, this study found that the majority of the Chinese provinces had a stable spatial structure of carbon emissions. Eighteen provinces had shorter than average time path lengths in 1995-2001 and 2002-2014. The majority of the southern provinces showed a fluctuating spatial dependence with increasing amplitude over time, while most of the northern provinces showed a relatively stable trend; (3) according to the directional Moran scatter plot, the number of provinces that showed the same trend decreased from 13 in 1995-2001 to 10 in 2002-2014, indicating that the spatial coherence of carbon emissions change at the provincial level had weakened; (4) spatial correlation patterns and clustering of carbon emissions by energy consumption at the provincial level were relatively stable and showed certain degree of path-dependence or lock-in character; (5) carbon emissions gravity center was between 113.739° ~114.324° E, 34.475° ~35.036°N and was moving to the northwest. The spatial distribution of provincial emissions presented a northeast-southwest pattern, and had the tendency of shifting to a north-south pattern. The focus of carbon emission reduction in China is to accelerate the development of clean energy, improve energy efficiency, promote the optimization and upgrading of energy and industrial structures in all provinces, make differentiated carbon emission reduction policies for different provinces, and establish carbon trading market.