Green tide is a common marine ecological disaster in offshore China. In order to use the UAV RGB optical camera to accurately monitor the green tide and establish a fast extraction index for green algae in high-resolution RGB optical images. A new index is proposed to enhance the signal of floating green algae. A virtual baseline is formed in the green and red bands, and the line-height of the blue band signal under this virtual baseline is the red-green band virtual baseline floating green algae index (RG-FAH). In addition, representative UAV images under different conditions are used to compare with other vegetation indices for verification. The experimental results show that the accuracy and kappa of RG-FAH under different conditions are all above 0.91. Under normal and overexposure conditions and the extraction of large patches of algae, RG-FAH appears to be comparable to GB, yet it is more beneficial than GB and other indices in terms of sun glitter tolerance and small patches of algae extraction. The RG-FAH index proposed in this study has potential application value in monitoring green algae and similar floating green plants in seawater. It can also provide effective information support for the monitoring and management of green tide.