Remote sensing technology can be used to estimate the leaf area index (LAI) value of crops rapidly and harmlessly. The purpose of this study is to research the accuracy, reliability, and adaptability of the LAI using unmanned aerial vehicle (UAV) multispectral remote sensing. During a summer maize-fertilizer cross test, the LAI and multispectral images captured by a six-rotor UAV with a MicaSense RedEdge-M camera (which has five high-resolution channels: blue, green, red, red edge, and near infrared) were collected at the jointing, tasseling, and maturity stages of the maize. The normalized differential vegetation index (NDVI), optimized soil adjusted vegetation index (OSAVI), enhanced vegetation index (EVI), and normalized differential red edge index (NDRE) were calculated at each stage. The correlation between these metrics and the LAI were analyzed and their values were established based on the multispectral images at different growth stages. Then, an LAI model for each growth stage was established. After the accuracy of these models was tested using independent data, a maize LAI estimation map was made by processing each pixel in the maize multispectral image using these models. The results indicate the following: 1) There is a high correlation between the LAI and the NDVI, OSAVI, EVI, and NDRE values at the jointing, tasseling, and maturity stages. 2) LAI estimation models were established based on OSAVI, NDRE, and NDRE for the jointing, tasseling, and maturity stages, respectively. They had decision coefficient values (R2) of 0.549, 0.753, and 0.733, respectively, and the R2 of the verification models were 0.907, 0.932, and 0.926, respectively. The predicted and measured values at different growth stages had relative error values of 8.57, 8.37, and 9.24 and root-mean-squared error values of 0.104, 0.087, and 0.091, respectively. 3) The spatial distribution of the LAI at field scale was mapped by the LAI estimation models at each growth stage, yielding R2 values of 0.883, 0.931, and 0.867 and relative error values of 9.17, 8.86, and 9.32, respectively. Therefore, the LAI map reflected the real-world spatial distribution pattern of the LAI in the maize fields well. The established agricultural UAV remote sensing monitoring system provides accuracy, reliability, and adaptability for precision agriculture applications as well as the corresponding retrieval models for studying the feasibility of estimating the LAI during different growth stages.