The multi-variable grey prediction model represented by the GM(1,N) model is an important causal relationship forecasting model. However, the GM(1,N) and its improved models believe that the development trend of the dependent variable sequence is only related to its own lag term and independent variables while ignoring the development trend of the dependent variable sequence with time. For this, a multi-variable DGMTP(1,N,α ) prediction model with time polynomial is proposed, and the value of parameter α is solved by debugging method. It is theoretically proved that the DGMTP(1,N, α ) model can achieve mutual transformation with the multi-variable GM(0,N) model, GM(1,N) model, DGM(1,N) model and the uni-variable GM(1,1) model, DGM(1,1) model, NDGM(1,1) model by adjusting the parameter values. To illustrate the performance of the DGMTP(1,N,α ) model, the new model is used to simulate and predict the air quality index in Zhengzhou city. The simulation and prediction results of the DGMTP(1,N,α ) model are compared with those of other grey and non-grey prediction models. Results show that the DGMTP(1,N,α ) model has evidently superior performance to other prediction models; this is because the DGMTP(1,N,α ) model avoids the large sample requirement of the non-grey prediction model in the modeling, avoids the jumping error in parameter estimation and application, and considers the time development trend of dependent variable sequence, which fully proves that the structure of the DGMTP(1,N,α ) model is reasonable and practicable.