The accumulated generation is an important part of grey prediction model, which helps mine information and finds the rule in sequence. According to the axiom of new information priority using in grey systems, new accumulated generation operator with parameter is defined, and then the new information priority accumulated grey discrete model (NIPDGM (1,1)) is constructed. Based on four kinds of error minimization criterions (mean squared error, mean absolute error, mean relative squared error, and mean absolute percentage error), the parameters optimization steps are presented. Through numerical simulating, the information weight in NIPDGM (1,1) model with different error criterions is studied. The result shows that the four kinds of optimization form for information weight are almost identical in sequence accumulated generation process. In the empirical analysis, expressway soft soil roadbed settlement and energy consumption problems in Jiangsu province are taken as examples, and the NIPDGM (1,1) modeling is used for two cases. In order to compare the modeling accuracy of new model, other grey model and some artificial intelligence models are also adopted for two cases, such as grey model(GM (1,1)), grey opposite model (GOM(1,1)), grey reciprocal model(GRM(1,1)), discrete grey model(DGM(1,1)), radial basis function(RBF) neural network, support vector machine (SVM) and so on. The results show that the information weights (or the parameter in accumulated generation) are not subjected to the different error minimization methods, which is consistent with the numerical simulating experiment. Compared with GOM (1,1) model, GRM(1,1)model, GM(1,1) model, DGM(1,1)model, grey model with time power (GM (1,1, t²)), and unbiased GM (1,1) power model, NIPDGM (1,1) model has a higher modeling precision in simulating and forecasting period for roadbed settlement. Among RBF neural network, grey accumulation generation RBF neural network (GRBF), support vector machine (SVM), grey accumulated generation support vector machine (GSVM) and NIPDGM (1,1) model for energy consumption modeling, the NIPDGM (1,1) model has a lager error in simulating period, but the smaller error in forecasting period, which indicates that the NIPDGM (1,1) model exhibits better generalization ability. The new accumulated generation operator can also be combined with other grey model, so as to enhance the model accuracy.