This paper focuses on the prediction algorithm of time-to-go for velocity-uncontrollable vehicles flying towards a target position in three-dimensional space. A novel prediction algorithm based on cubic polynomial fitting is proposed, which simplifies the nonlinear differential equation model into a linearly solvable polynomial model, and then obtains the mathematical expressions for the time-to-go and average velocity, thereby achieving precise prediction. Moreover, by replacing the constant velocity assumption with the time-varying average velocity, the prediction accuracy of the time-to-go has been improved under the time-varying velocity model. Additionally, polynomial expressions are utilized to generate subsequent guidance commands, and the computational load on onboard systems is reduced. The effectiveness of the proposed method in terms of prediction accuracy and its broad applicability in impact time control guidance are validated through multiple simulation scenarios.