By combining an optimally-trained classifier with a simple spectrometric system developed by ourselves, the sweetness of apples has been classified nondestructively with high accuracy and precision. A simple spectrometric system is practical in principle, but its manufacturability and reproducibility were somehow limited in the previous studies because they were based on discrete components such as filters or LEDs. High manufacturability and reproducibility of our developed system were already reported, but the performance of sweetness grading was not examined. In this study, the best performance of 91.3% accuracy and 91.5% precision was obtained from a discriminant analysis (DA) model that was trained with the spectral response of apple at five wavebands (535, 680, 730, 760, and 900 nm) selected with a sequential forward selection (SFS) algorithm. The performance level was superior to that of the previous studies on their simple spectrometric systems. From the achieved performance and evaluated computational complexity, it can be concluded that the combination of a machine learning-based classifier and our simple spectrometric system is effective for fruit quality assessment and especially suitable for cost-effective applications.