Refractive-index random fluctuations in the oceanic turbulence channel can cause wavefront distortions and intermodal crosstalk of vortex beams, thereby reducing the transmission probability of orbital angular momentum modes and undermining the stability of underwater optical communication systems. To address the limitations of the conventional GS algorithm—namely, its reliance on the far-field Fraunhofer diffraction assumption, its inability to characterize Fresnel diffraction in short-range underwater propagation, and its tendency to get trapped in local optima—an improved GS algorithm for underwater vortex-beam wavefront correction is proposed. In this algorithm, Fresnel forward/inverse diffraction is used to replace Fraunhofer diffraction; the amplitude of an ideal Laguerre-Gaussian vortex beam is introduced as an amplitude constraint; and a restricted region together with a negative-feedback mechanism is incorporated to achieve rapid and stable convergence. The method is validated theoretically and experimentally. Simulation results show that under moderate turbulence, the transmission probability of a vortex beam with topological charge L=1 increases from 0.40 to 0.98. Across variations in topological charge, propagation distance, turbulent kinetic energy dissipation rate, mean-square temperature dissipation rate, and temperature-salinity ratio, the improved GS algorithm consistently shows better robustness and higher correction accuracy than the traditional GS algorithm. Results based on simulating ocean turbulence using a spatial light modulator indicate that the improved GS algorithm converges in about 120 iterations on average, and the intensity correlation coefficient increases from 0.64 to 0.82. Compared with the conventional GS algorithm, the transmission probability is improved by approximately 20%, the convergence speed by about 25%, and the intensity correlation coefficient by roughly 3.8%. In water-tank experiments, the average intensity correlation coefficient and variance are 0.77 and 8.2×10-5 before correction; 0.79 and 3.23×10-5 after correction using the traditional GS algorithm; and further improved to 0.80 and 1.4×10-5 with the proposed algorithm. These results demonstrate that the proposed method exhibits superior robustness under a wide range of turbulence parameters, providing a useful reference for wavefront correction in underwater vortex-beam optical communication systems.