Precise prediction of carbon prices is not only of significance for policy formulation and investment decisions, but also helpful to the carbon finance market development. Considering the non-stationary and nonlinearity characteristics inherent in the carbon price, this study proposed a novel hybrid model named ICEEMDAN-TGARCH/LSTM(CS)-LSTM(CS), in which the ICEEMDAN (improved complete ensemble empirical mode decomposition with adaptive noise) is applied to decompose the carbon price original series into several subcomponents, then the subcomponents are identified according to comprehensive contribution index (CCI) and divided into short-term, long-term and trend components. TGARCH(threshold generalized auto-regressive conditional heteroscedasticity) is chosen for the short-term components forecasting, while LSTM (long-short term memory) neural network model with hyper-parameters optimized by cuckoo search (CS) algorithm is selected to forecast other components and combine all the forecasting sequences. The empirical results Hubei carbon emission trading market indicated that the proposed model outperformed other benchmark models with the lowest prediction error, meaning that the hybrid model proposed by us can be an effective and accurate tool for carbon price forecasting. It provides effective information for regulatory authorities and enterprises to make decisions.