It is generally feasible to classify different species of vegetation based on remotely sensed images, but identification of different sub-species or even cultivars is uncommon. Tea trees (Camellia sinensis L.) have been proven to show great differences in taste and quality between cultivars. We hypothesize that hyperspectral remote sensing would make it possibly to classify cultivars of plants and even to estimate their taste-related biochemical components. In this study, hyperspectral data of the canopies of tea trees were collected by hyperspectral camera mounted on an unmanned aerial vehicle (UAV). Tea cultivars were classified according to the spectral characteristics of the tea canopies. Furthermore, two major components influencing the taste of tea, tea polyphenols (TP) and amino acids (AA), were predicted. The results showed that the overall accuracy of tea cultivar classification achieved by support vector machine is higher than 95% with proper spectral pre-processing method. The best results to predict the TP and AA were achieved by partial least squares regression with standard normal variant normalized spectra, and the ratio of TP to AA—which is one proven index for tea taste—achieved the highest accuracy (RCV = 0.66, RMSECV = 13.27) followed by AA (RCV = 0.62, RMSECV = 1.16) and TP (RCV = 0.58, RMSECV = 10.01). The results indicated that classification of tea cultivars using the hyperspectral remote sensing from UAV was successful, and there is a potential to map the taste-related chemical components in tea plantations from UAV platform; however, further exploration is needed to increase the accuracy.