The current precession period extraction methods are analyzed in this paper. Considering their low accuracy and stability in low SNR environment, a new method is proposed based on the double average magnitude difference function (DAMDF). Utilizing the current methods' same period characteristic with the original data and the average argument's decay characteristic with the increase of step, the result of DAMDF has just only one peak, so that it can overcome the unfavourable influence of the frequency demultiplication as well as restrain the interference brought about by frequency multiplication and noise. Simulation results present that the new method can enhance the accuracy and stability of precession period estimation greatly in low SNR environment.