Accurate carbon price forecasting is of great significance for policy-makers and market participants. However, previous studies only focus on point-valued forecasting and ignore the importance of interval carbon price forecasting. In fact, interval-valued forecasting contains more information and can measure the uncertainty and variability of carbon price. Thus, to predict interval carbon price accurately, we propose a novel interval decomposition ensemble model based on multivariate variational mode decomposition (MVMD) and interval multilayer perceptron (iMLP) optimized by Jaya algorithm. Firstly, MVMD is used to decompose the original interval carbon price series into several sub-series. Secondly, iMLP optimized by Jaya algorithm is constructed to predict each sub-series of the above step. Finally, forecasting results of each sub-series are aggerated into the ultimate predictions of interval carbon price by linear addition. The interval carbon price data from two carbon markets in China are utilized to validate the effectiveness of the proposed model. Experimental results reveal that the proposed model outperforms all the benchmark models and the average values of the interval U of Theil statistics (UI) and the interval average relative variance (ARVI) in two datasets are 0.3003 and 0.0569, respectively. Overall, the proposed model can be used as an effective tool for future interval carbon price forecasting. •Propose a novel model to predict interval carbon price: MVMD-Jaya-iMLP.•MVMD is applied to decompose the original interval carbon price.•Jaya algorithm is employed to optimize the initial weights and biases of iMLP.•MVMD improves the forecasting accuracy.•The proposed model outperforms other benchmark models.