The forecast of short-term time series data is of practical value when enterprises face global competition. However, to successfully make it is difficult because of the limited data size. Therefore, it is considered as a great challenge to improve the preciseness of predictions when dealing with such limited data. In decades, the Grey Model (GM) has significant developments in theories and applications in real world. However, the accuracy of GM can be improved in some ways, and one of these is to find the suitable background values. To achieve it, the Adaptive Grey Model was proposed by taking the occurring trend of data into consideration, and the experimental results demonstrated better preciseness than those of some other improved GM models. In fact, setting the suitable background values of GM can be treated as the process in searching the optimal solutions. This paper thus employs the genetic algorithm (GA) to achieve this by taking the parameters generated by AGM as the initial solutions to build a more accurate model, called GAAGM(1,1).