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Aiming at the poor prediction performance of the traditional GM(1,N) model, this paper proposes the GM(1,N) model with expression optimization: firstly, unknown parameters are introduced into the coefficient matrix of the traditional GM(1,N) model to obtain the model expression with unknown parameters: Then the average relative error function with unknown parameters is constructed: Finally, the particle swarm optimization algorithm is used to obtain the parameter column with the smallest average relative error. Taking the carbon emission of the logistics industry in Hubei Province as an example, this paper forecasts the carbon emission by using the traditional GM(1,N) model, GM(1, N) model with background value optimization, and GM(1, N) model with expression optimization. By comparing and analyzing the prediction results of the three models, it is concluded that GM(1,N) model with expression optimization has better prediction performance. [ABSTRACT FROM AUTHOR]