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Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation,which makes the parameters unable to be adjusted according to the data characteristics of the actual problems.The results about fractional derivative multivariable grey models are very few at present.In this paper,a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q,N) is proposed.First,the Caputo fractional difference is used to discretize the model,and the least square method is used to solve the parameters.The orders of accumulations and differential equations are determined by using particle swarm optimization (PSO).Then,the analytical solution of the model is obtained by using the Laplace transform,and the convergence and divergence of series in analytical solutions are also discussed.Finally,the CFGMC(q,N) model is used to predict the municipal solid waste (MSW).Compared with other competition models,the model has the best prediction effect.This study enriches the model form of the multivariable grey model,expands the scope of application,and provides a new idea for the development of fractional derivative grey model.