A portable spectrometric system for nondestructive assessment of the soluble solids content (SSC) of fruits for practical applications has been proposed and its performance has been examined by an experiment on quantitative prediction of the SSC of apples. Although the spectroscopic technique is a powerful tool for predicting the internal qualities of fruits, its practical applications are limited due to its high cost and complexity. In the proposed system, the spectra of apples were collected by a simple optical setup with a cheap pre-calibrated multispectral chipset. An optimal multiple linear regression model with five wavebands at 900, 760, 730, 680, and 535 nm revealed the best performance with the coefficient of determination of prediction and the root mean square error of prediction of 0.861 and 0.403 °Brix, respectively, which was comparable to that of the previous studies using dispersive spectrometers. Compared with previously reported systems using discrete filters or light emitting diodes, the proposed system was superior in terms of manufacturability and reproducibility. The experimental results confirmed that the proposed system had a considerable potential for practical, cost-effective applications of the SSC prediction, not only for apples but also for other fruits.