The background value is one important factor that affects the accuracy of the gray theoretical modeling. The dynamic series model is constructed according to the gray system theory modeling mechanism and the data accumulated generating operation with non-homogeneous gray exponentially. A new GM(1,1) model background value optimization method is proposed based on integral geometric meaning by using the idea of function approximation and the combined trapezoid formula. The example shows that the prediction accuracy of GM(1,1) model is significantly improved by the using the optimized background value formula.