Abstract:A modified algorithm based upon the Nelson-Zarchan’s method is presented for the Lambert’s problem of the fixed-time transfer orbital. A nonlinearity approximation function is set up with the bicubic spline interpolation function, which includes the flight time for transferring, initial and final position vectors and the flight path angle. Then the approximation function provides a new way to initialize the value of the flight path angle, so as to speed up the calculate process. With the hypothesis testing and simulation comparison, it is shown that the modified flight path angle algorithm has competitive and better calculating speed.