Prediction for footprint of incoming hypersonic glide reentry vehicle as a defensive party has such problems as insufficient prior information and high timeliness requirement for solution. A fast prediction method of footprint based on optimal flight hypothesis was proposed:only if the position, velocity and maximum lift-drag ratio of the target at the current time are known (which can be obtained by real-time trajectory estimation based on radar detection data), based on the equilibrium glide hypothesis and the Egers solution of the maximum cross range, the coordinates of the maximum longitudinal range and cross range end points can be obtained respectively; then in the two-dimensional plane of longitude and latitude, the footprint can be approximated as a semi-elliptic area with the intersection of the two maximum cross range end points as the short axis and the distance from the maximum longitudinal range end point to the short axis as the half-long axis. The simulation results show that, compared with the traditional numerical optimization method and the constant bank angle method, the proposed method has the advantages of less prior information, higher accuracy and less computation, and can meet the real-time requirements.