To overcome the theoretical deficiency of the segmented Knothe time function, and to enlarge its range of application and improve its prediction accuracy, this paper conducts further study of the existing problems of the segmented Knothe time function through theoretical analysis and comparative study. The corresponding improvement method is given. And a new segmented Knothe time function is established, which has a broader applicable scope and higher prediction precision in the practical engineering. The results show that the established model successfully solves the problem of the function value differs from the theoretical value in the place of subsection point, and the problem of the time function value cannot eventually converge to 1. The new model of time function does not rely on certain restrictions of the parameter selection. The applicability of the new time function to dynamic prediction for different geological and mining conditions is enhanced. Through the prediction comparison between the new segmented time function and the original time function, it is shown that the prediction accuracy is improved significantly while using the new time function. In addition, the final prediction value of surface subsidence will stabilize and no longer change with the extension of prediction time.