Chlorophyll a (chl-a) concentration is an important parameter for evaluating the degree of water eutrophication. Monitoring it accurately through remote sensing is thus of great significance for early warnings of water eutrophication, and the inversion of water quality from UAV images has attracted more and more attention. In this study, a regression method to estimate chl-a was proposed; it used a small multispectral UAV to collect data and took the vegetation indices as intermediate variables. For this purpose, ten monitoring points were selected in Erhai Lake, China, and two months of monitoring and data collection were conducted during a cyanobacterial bloom period. Finally, 155 sets of valid data were obtained. The imaging data were obtained using a multispectral UAV, water samples were collected from the lake, and the chl-a concentration was obtained in the laboratory. Then, the images were preprocessed to extract the information from different wavebands. The univariate regression of each vegetation index and the regression using band information were used for comparative analysis. Four machine learning algorithms were used to build the model: support vector machine (SVM), random forest (RF), extreme learning machine (ELM), and convolutional neural network (CNN). The results showed that the effect of estimating the chl-a concentration via multiple regression using vegetation indices was generally better than that via regression with a single vegetation index and original band information. The CNN model obtained the best results (R² = 0.7917, RMSE = 8.7660, and MRE = 0.2461). This study showed the reliability of using multiple regression based on vegetation indices to estimate the chl-a of surface water.