Abstract: In 2021, the National People's Congress put "peak carbon dioxide emissions" and "carbon neutralization" into the government work report for the first time, and so carbon emissions arouses great concern from all walks of life. Based on the relevant data from 1979 to 2017, this paper uses Morlet wavelet analysis (wavelet correlation, continuous wavelet transform, wavelet partial coherence, wavelet re-coherence, etc.) to study the relationship among the four factors of foreign direct investment, renewable energy consumption, economic growth and carbon dioxide emission in China, and points out the law that the relationship among the four variables changes with frequency and time. The study reveals that although there is no consistent relation among the four variables in the time domain, there is obvious wavelet coherence in the frequency domain, as well as strong leading and lagging relation, which supports the view that foreign direct investment and renewable energy consumption are helpful to improve China's economic development from an economic point of view. The study also suggests that in the medium and long term, foreign direct investment will aggravate the environmental degradation of our country, so the government must give overall consideration to economic development and environmental protection, and deal with the possible consequences of environmental degradation from a strategic perspective.