The sugar content and firmness of red globe grapes are important indicators for evaluating their quality. This study explores nondestructive detection methods and best prediction models for determining the sugar content and firmness of red globe grapes based on hyperspectral imaging technology. The hyperspectral images of 213 samples, in the wavelength range of 400-1000 nm, are collected in three placement orientations (horizontal, fruit stalk-side down, and fruit stalk-side up). The optimal orientation for spectral imaging is compared and analyzed, and subsequently the spectrum is preprocessed in the optimal orientation. Several preprocessing methods, i.e., genetic algorithm (GA), successive projections algorithm (SPA), competitive adaptive reweighed sampling (CARS) algorithm, and uninformative variable elimination algorithm (UVE), are applied to the images to extract characteristic wavelengths from the original spectra. Using chemometrics methods, combined with either partial least squares regression (PLSR), least squares support vector machine (LSSVM), and random forest (RF) analysis based on full spectra and characteristic wavelengths, several protocols are established to mathematically predict the sugar content and firmness of red globe grapes from the images. Results show that the sugar and firmness model based on RF performs the best. The optimal model for predicting sugar content proves to be RF optimized by GA (GA-RF), with corrected-set correlation coefficient (R_c) and predicted-set correlation coefficient (R_p) values of 0.969 and 0.928, respectively, and corrected-set root-mean-square error (RMSEC) and predicted-set root-mean-square error (RMSEP) values of 0.266 and 0.254, respectively. The optimal model for predicting firmness proves to be RF optimized by moving-average method and SPA (MA-SPA-RF), with R_c and R_p values of 0.961 and 0.932, respectively, and RMSEC and RMSEP values of 2.119 and 1.634, respectively. These results prove the sugar content and firmness of red globe grapes can be nondestructively predicted via hyperspectral imaging.