The invention discloses a strapdown inertial navigation method of dual quaternion based on a frequency domain analysis method. The invention is designed aiming at the following problem: various errors of carrier movement can not be fully compensated because of polynomial fitting of the angular velocity and the specific force of the carrier in the traditional time-domain strapdown inertial navigation algorithm. The principle of the invention is as follows: carrying out smooth continuation and discrete Fourier transform on the increment signal output by an inertial navigation device and the navigation information obtained in the solving process by utilizing the frequency domain analysis method, then solving the spectrum signal obtained through transform by utilizing the strapdown inertial navigation algorithm of dual quaternion realized in the frequency domain and finally carrying out inverse Fourier transform on the signal obtained by solving to obtain the navigation solution in the time domain. Compared with the existing time-domain strapdown inertial navigation methods of dual quaternion, the method is characterized by taking full advantage of the information of the signal output by the inertial navigation device in each frequency range and having higher precision under high dynamic environment.