Most existing grey fractional-order multivariable models adopt the same fractional order for both the system term and the driving term, ignoring the impact of varying fractional orders of the driving term on model accuracy. To further improve the fitting and prediction accuracy of grey multivariable prediction models involving fractional orders, a novel non-equal-order discrete nonlinear grey multivariable prediction model is proposed by introducing non-equal fractional orders and nonlinear functions. The modeling mechanism, parameter estimation method and recursive time response formula of the proposed model are investigated, and the properties of the model under several special values of parameters are discussed. Finally, the proposed model is applied to predict the port cargo throughput of Jiangsu Province, with the fitting accuracy of 1.05% and the prediction accuracy of 1.91%. The results show that the fitting and prediction accuracy of the proposed model is significantly superior to that of the benchmark models, which verifies its applicability and effectiveness.