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Recently, with the development of European carbon futures markets, the complex dynamic relationship between price and volume has become the focus of energy research area. In our research, we applied multifractal detrended cross-correlation analysis method (MF-DCCA) to investigate the cross-correlation and multifractality between price and volume in European carbon futures markets. Firstly, the analysis of basic statistics show that the European carbon futures market has obvious non-normal, peak-heavy-tailed distribution, which does not satisfy the normal distribution hypothesis in the efficient market. Secondly, through multifractal detrended cross-correlation analysis, we conclude that trading price and volume relationship in European carbon futures markets has a non-linear dependence. Thirdly, we find the existence of power-law cross-correlations between price and volume in European carbon futures markets. Finally, the relationship between price and volume is non-linear. After random rearrangement and phase treatment of correlation coefficients, the long-range correlation of small fluctuations and large fluctuations and the fat tail distribution of series are the reasons for the formation of multifractality. [ABSTRACT FROM AUTHOR]