This　paper　studies　the　carbon　price　fluctuation　in　China　through　the　adaptive　Fourier　decomposition　(AFD).　Apart　from　the　transient　time-frequency　distribution　of　the　original　AFD　model,　we　also　reconstruct　the　mono-components　of　this　model　to　obtain　the　components　in　different　time-frequency　scales.　Our　empirical　results　based　on　the　carbon　price　in　Hubei　Province　demonstrate　that　there　are　three　periods　when　the　price　fluctuates　dramatically,　mainly　affected　by　the　governmental　policies　about　carbon　emission　and　the　development　of　clean　energies,　as　well　as　the　outbreak　of　COVID-19.　Furthermore,　the　fluctuations　of　the　price　in　the　three　identified　periods　are　reflected　in　different　scales.　The　comparison　of　the　decomposition　results　and　those　of　EMD　and　VIVID　shows　that　the　AFD　performs　best　in　absorbing　the　price＇s　useful　information　extracted　through　all　these　methods.　(C)　2021　The　Authors.　Published　by　Elsevier　B.V.