The invention discloses a space manipulator continuous trajectory tracking method. The method includes the steps of firstly, controlling the tail end of a manipulator through an inverse generalized Jacobi method to track a known trajectory, utilizing a larger amount of calculation to obtain a more accurate solution due to the fact that the accuracy of results of the method is inversely proportional to the numerical integration step, and combining a Milne-Hamming linear multi-step prediction correction method with the method to improve the accuracy of the calculation of a fixed step size; then, calculating the four values before the fifth step of the Milne-Hamming algorithm through a Runge-Kutta method. The space manipulator continuous trajectory tracking method can accurately complete continuous trajectory tracking of the space manipulator in task space.