The disclosure discloses a latitude-free initial alignment method under a swaying base based on gradient descent optimization. Firstly, swaying base latitude-free alignment is regarded as a Wahba attitude determination problem to inhibit device noise interference, and an objective function is established based on a gravitational acceleration vector under an earth system; then an exact solution of the objective function is obtained through a gradient descent optimization method, and inertial system conversion quaternion estimation is achieved under the latitude-free condition; and finally, an attitude quaternion is determined by only using information of an accelerometer and a gyroscope of a strapdown attitude heading reference system, and therefore latitude-free initial alignment under the swaying base is achieved. The disclosure can solve the problem that initial alignment cannot be accomplished with unknown latitude under the swaying base, and thus the application range of the strapdown attitude heading reference system is ensured.