  The classical GM(1,1) model is an efficient tool to {make accurate forecasts}
with limited samples. But the accuracy of the GM(1,1) model still needs to be
improved. This paper proposes a novel discrete GM(1,1) model, named ${\rm
GM_{SD}}$(1,1) model, of which the background value is reconstructed using
Simpson formula. The expression of the specific time response function is
deduced, and the relationship between our model} and the continuous GM(1,1)
model with Simpson formula called ${\rm GM_{SC} }$(1,1) model is systematically
discussed. The proposed model is proved to be unbiased to simulate the
homogeneous exponent sequence. Further, some numerical examples are given to
validate the accuracy of the new ${\rm GM_{SD}}$(1,1) model. Finally, this
model is used to predict the Gross Domestic Product and the freightage of
Lanzhou, and the results illustrate the ${\rm GM_{SD}}$(1,1) model provides
accurate prediction.
