Prompted by alleviating the random perturbation of underwater channel and enhancing the performance for the orbital angular momentum (OAM) -based underwater wireless optical communication (UWOC), the quasi-Airy Hypergeometric-Gaussian (QAHyGG) vortex beam is first proposed and demonstrated. Moreover, an underwater channel model is first modified for more accurate simulated results of the propagation property of various beams. Based on the modified model, the transmission and communication performance of three different OAM-carrying beams (the Gauss vortex (GV) beam, the Hypergeometric-Gaussian (HyGG) vortex beam, and the QAHyGG vortex beam) are comparatively studied. In addition, the parameters optimization of the QAHyGG vortex beam is made for further enhancing the average capacity. The results show that the QAHyGG vortex beam exhibits higher received power and lower crosstalk probability under different channel conditions. The average capacity of the QAHyGG vortex beam has enhanced by ∼8% and ∼27% compared with the HyGG vortex beam and the GV beam at 100m, respectively. The QAHyGG vortex beam is more suitable in an OAM-based UWOC system with a limited-size receiving aperture or lower transmit power. Besides, the average capacity will improve effectively at longer distances with the optimized beam parameters. These research results can provide advances in designing the practical OAM-based UWOC system.