Carbon pricing is regarded as a crucial enabler for an accelerated low-carbon energy economy transformation to achieve temperature control targets. This paper studies carbon price forecasting considering historical carbon price series as an influencing factor. A hybrid model of a kernel-based extreme learning machine (KELM) optimized by the bat optimization algorithm based on wavelet transform is proposed. Firstly, the wavelet transform is used to eliminate the high-frequency components of the previous day’s carbon price data to improve the accuracy of prediction. Then, the partial auto-correlation function (PACF) is applied to analyse the correlation among historical carbon prices to select the inputs for the forecasting model. Additionally, adding a kernel function improves to some extent the fitting accuracy and stability of the traditional extreme learning machine. Finally, the parameters of the KELM model are optimized by the bat optimization algorithm. Two types of carbon prices in the China ETS were used to examine the forecasting ability of the proposed hybrid methodology. The empirical results show that the proposed hybrid methodology is more robust than other comparison models for carbon price forecasting.