In this paper, a new and robust method is proposed to realize high-fidelity non-line-of-sight (NLOS) optical information transmission through turbid water around a corner. A series of 2D random amplitude-only patterns are generated by using the zero-frequency modulation method, which are used as optical information carriers. The laser beam modulated by random amplitude-only patterns propagates through turbid water, and the wave diffused by turbid water is further reflected around a corner. A single-pixel detector is used to collect light intensity at the receiving end. To demonstrate feasibility and effectiveness of the proposed NLOS free-space optical information transmission system, many optical experiments are conducted. The proposed method is fully verified by using different turbid water conditions, different separation distances around a corner and different detection angles of the single-pixel detector. Optical experimental results demonstrate that the proposed method is able to achieve high fidelity and high robustness for free-space optical information transmission through turbid water. Even when there is an obstacle behind turbid water, high-fidelity free-space optical information transmission is still realized by using the proposed method. In addition, the proposed method possesses a wide detection range at the receiving end, which is of great significance in practical applications. The proposed method is a promising application for NLOS free-space optical information transmission.