Unmanned aerial vehicle (UAV) remote sensing technology can be used for fast and efficient monitoring of plant diseases and pests, but these techniques are qualitative expressions of plant diseases. However, the yellow leaf disease of arecanut in Hainan Province is similar to a plague, with an incidence rate of up to 90% in severely affected areas, and a qualitative expression is not conducive to the assessment of its severity and yield. Additionally, there exists a clear correlation between the damage caused by plant diseases and pests and the change in the living vegetation volume (LVV). However, the correlation between the severity of the yellow leaf disease of arecanut and LVV must be demonstrated through research. Therefore, this study aims to apply the multispectral data obtained by the UAV along with the high-resolution UAV remote sensing images to obtain five vegetation indexes such as the normalized difference vegetation index (NDVI), optimized soil adjusted vegetation index (OSAVI), leaf chlorophyll index (LCI), green normalized difference vegetation index (GNDVI), and normalized difference red edge (NDRE) index, and establish five algorithm models such as the back-propagation neural network (BPNN), decision tree, naïve Bayes, support vector machine (SVM), and k-nearest-neighbor classification to determine the severity of the yellow leaf disease of arecanut, which is expressed by the proportion of the yellowing area of a single areca crown (in percentage). The traditional qualitative expression of this disease is transformed into the quantitative expression of the yellow leaf disease of arecanut per plant. The results demonstrate that the classification accuracy of the test set of the BPNN algorithm and SVM algorithm is the highest, at 86.57% and 86.30%, respectively. Additionally, the UAV structure from motion technology is used to measure the LVV of a single areca tree and establish a model of the correlation between the LVV and the severity of the yellow leaf disease of arecanut. The results show that the relative root mean square error is between 34.763% and 39.324%. This study presents the novel quantitative expression of the severity of the yellow leaf disease of arecanut, along with the correlation between the LVV of areca and the severity of the yellow leaf disease of arecanut. Significant development is expected in the degree of integration of multispectral software and hardware, observation accuracy, and ease of use of UAVs owing to the rapid progress of spectral sensing technology and the image processing and analysis algorithms.