In this study, we propose an underwater ghost-imaging scheme using a modulation pattern combining offset-position pseudo-Bessel-ring (OPBR) and random binary (RB) speckle pattern illumination. We design the experiments based on modulation rules to order the OPBR speckle patterns. We retrieve ghost images by OPBR beam with different modulation speckle sizes. The obtained ghost images have a better contrast-to-noise rate compared to RB beam ghost imaging under the same conditions. We verify the results both in the experiment and simulation. In addition, we also check the image quality at different turbidities. Furthermore, we demonstrate that the OPBR speckle pattern also provides better image quality in other objects. The proposed method promises wide applications in highly scattering media, atmosphere, turbid water, etc.