Green water generated by random waves on a fixed, simplified geometry model structure was measured in a large wave basin. The velocity field of the flow that is aerated and highly turbulent was quantified using the bubble image velocimetry (BIV) technique. BIV utilizes shadow textures created by air-water interfaces as tracers in backlit images recorded by a high speed camera. The tracers in consecutive images are then cross-correlated to obtain the corresponding two-dimensional velocities. Random waves were generated by the JONSWAP spectrum with a significant wave height close to the freeboard. An image-based triggering method was employed to detect the green water events and trigger image acquisition. A total of 179 green water events were collected and categorized into three different types, based on the flow behavior. That includes the collapse of overtopping wave, fall of bulk water, and breaking wave crest. Statistical distributions of maximum green water velocities under random waves were developed, while the lognormal distribution was found as the best fit. By modeling the green water as a dam break flow, the Ritter solution was found to be able to capture the horizontal velocity distribution for the random green water events. A prediction equation for the green water velocity distribution under random waves was also obtained.