In this paper, we consider the problem of estimating the trajectory of the ballistic object, especially the ballistic missiles, and its launch point based on radar measurements using promising deep learning technique-the Long-Short Term Memory(LSTM) Network. The conventional way of estimating the trajectories are solely based on the dynamic model of a missile to the Filter(KF). the implement Kalman However, since dynamics of missile change over the flight phases(boost, ballistic, reentry phase) and the flight phase of the missile would be difficult to differentiate using only radar observations, here we suggest a model-free method that utilizes the LSTM for the estimation. By implementing the suggested method, we can accurately estimate the trajectories and launch points of ballistic missiles only using the radar measurement without any consideration of the dynamics and parameters of the missile flight system.