The free-fight trajectory estimation by a single LEO satellite plays a key role in the space-based early warning system. An actual measurement function was established, and a polynomial approximation algorithm was proposed to reduce the computational amount of the batch algorithm of maximum-likelihood estimation (MLE). The approximate polynomial of the measurement function was evaluated at some deterministic instants to form pseudo measurement data. The raw measurement data were replaced by the pseudo ones to estimate the trajectory. The simulation results show that this new algorithm greatly reduces the computational amount, and can achieve the same accuracy performance as MLE.