The initial conditions of gray GM (1,1) model have an important influence on the accuracy of the model. In order to improve the accuracy of the grey model, an optimization method of initial condition is proposed. Firstly, the role of each component in the 1-AGO sequence is taken into account. So the weighted average of all components is chosen as the initial condition. Its weight is determined by the size of each component. Then, the error squared sum of the simulation sequence and original sequence is weighted based on the time weight sequence. Finally, the optimal problem is solved and the time parameter is calculated to establish the optimization model. Some examples are given to illustrate that the proposed optimization model is feasible and can improve the accuracy of the grey model effectively.