To address the issue of reduced measurement accuracy for vortex beam displacement in ocean turbulence, this paper proposes a vortex beam displacement measurement method based on the Gerchberg-Saxton（GS）algorithm. By reconstructing the original phase distribution of the vortex beam from distorted intensity profiles using the GS algorithm and performing cross-correlation matching with a pre-established turbulence channel template library, high-precision displacement localization is achieved. Simulation results show that the performance of this algorithm is inferior to traditional algorithms under no or weak turbulence conditions, but outperforms traditional algorithms under strong turbulence conditions; moreover, the larger the mode value of the Laguerre-Gaussian（LG）beam, the greater the mean square error in measurement.