The GM(1,1) model's prediction accuracy is significantly influenced by the accuracy of background value estimation. The traditional trapezoidal background value can only be applied to a specific data sequence. Therefore, this study proposes a GM(1,1) model background value reconstruction approach based on the combination of intelligent trapezoidal and variable weights in order to increase the model's application as well as its prediction accuracy. The trapezoidal background value function with slope and point position parameters is called model I. Then, a set of point position parameter sequences, with a new background value function is constructed, called model II. A genetic algorithm is utilized to seek for the values of the parameters to be determined in both models I and II. The results showed that for the exponential growth data series, model I and II have higher prediction accuracy compared to traditional models. For data sequences, taking the traffic volume series of a road from 2014 to 2023, the prediction accuracy of this paper's model I method can be improved by 0.3643 % and 0.2725 % compared with Deng's and Wang's models. The prediction accuracy of this paper's model II method has been further improved by 0.1075 % compared with that of model I.