For the problems of undefined time-delayed mechanism and low accuracy of multi-variable grey models, the deficiency of traditional multi-variable grey model is analyzed and a new multi-variable discrete grey model is proposed by introducing the time-delay coefficient. Then the methods of calculating the parameters are discussed. According to the sufficient and insufficient information about the time-delay coefficient, empirical analysis and particle swarm optimization algorithms are used to explore the estimation of time-delay coefficient, and the modeling procedure is proposed. Finally, the effectiveness of the proposed model is verified by the numerical simulation and actual examples. Results show that the propoved model can the forecasting problems on the multi-variable time-delayed system with small sample data.