The quality of fresh apple fruits is a major concern for consumers and manufacturers. Classification of these fruits according to their ripening stage is one of the most decisive factors in determining their quality. In this regard, the aim of this work is to develop a new method for non-destructive classification of the ripening state of Fuji apples using hyperspectral information in the visible and near-infrared (Vis/NIR) regions. Spectra of 172 apple samples in the range from 450 to 1000 nm were studied, which were selected from four different ripening stages. A convolutional neural network (CNN) model was proposed to perform the classification of the samples. The proposed method was compared with three alternative methods based on artificial neural networks (ANN), support vector machines (SVM), and k-nearest neighbors (KNN). The results revealed that the CNN method outperformed the alternative methods, achieving a correct classification rate (CCR) of 96.5%, compared with an average of 89.5%, 95.93%, and 91.68% for ANN, SVM, and KNN, respectively. These results will help in the development of a new device for fast and accurate estimation of the quality of apples.