Aiming at the non-equidistant problems, an optimized non-equidistant GM(1,1)$ model is designed based on the principle of new information priority. After analyzing the defects of previous optimized initial conditions, a new initial condition is designed by using the weighted sum of each component in 1-AGO sequence based on the principle of the new information priority. In order to show the modified effects of the new data points, the weight of each component in this newly proposed initial condition is calculated based on its value. Under the premise of minimizing the square sum of the relative error between the original series and the forecasting sequences, the solution to the newly generating parameter is presented. To verify the effectiveness of the novel model, two cases of increasing and decreasing sequences are conductd. The experimental results show that the optimized model can make full use of the new information, so as to achieve better forecasts than the previous modified models.