Understanding the pathway of carbon emissions is an important basis for establishing a national climate strategy. In this paper, the change in China's economic carbon intensity since its accession to the World Trade Organization has been analyzed with a time series decomposition analysis method. Four phases with distinctive features are defined, and the significant fluctuations in China's economic carbon intensity after 2001 are explained in detail. From the phase-average perspective, the contributions of major factors to the economic carbon intensity change have evolved steadily, instead of through highly volatile change on a yearly basis, and the gradual changes have been caused mainly by the development of the industrial sectors. Induced by the new normal in economic development, the change of China's economic carbon intensity has entered a new phase driven by multiple factors with economic structural improvement being the most important contributor, as well as the continuingly, though decreasingly, important factor of energy efficiency.