The traditional GM(2,1) is to solve the time response coefficient under the condition that the simulated value is equal to the real value at the initial time and the last time, the intermediate time plays no role in determining the response coefficient, resulting in insufficient use of information. The paper focuses on the non-homogeneous GM(2,1), when solve for the time response coefficient，the real values of each moment are taken into comprehensive consideration, takes the target function into minimum. However, in order to avoid cumulative errors, all the coefficients in the time response equation, including the coefficients or constant terms that can be represented by the parameter are regarded as undetermined coefficients. Finally the formulas of time response coefficients under different conditions are derived. Examples show that the time response coefficient determined by the method has a high accuracy of simulation prediction