Designing computer-aided diagnosis (CAD) systems that can automatically detect ocular diseases (ODs) has become an active research field in the health domain. Although the human eye might have more than one OD simultaneously, most existing systems are designed to detect specific eye diseases. Therefore, it is crucial to develop new CAD systems that can detect multiple ODs simultaneously. This paper presents a novel multi-label convolutional neural network (ML-CNN) system based on ML classification (MLC) to diagnose various ODs from color fundus images. The proposed ML-CNN-based system consists of three main phases: the preprocessing phase, which includes normalization and augmentation using several transformation processes, the modeling phase, and the prediction phase. The proposed ML-CNN consists of three convolution (CONV) layers and one max pooling (MP) layer. Then, two CONV layers are performed, followed by one MP and dropout (DO). After that, one flatten layer is performed, followed by one fully connected (FC) layer. We added another DO once again, and finally, one FC layer with 45 nodes is performed. The system outputs the probabilities of all 45 diseases in each image. We validated the model by using cross-validation (CV) and measured the performance by five different metrics: accuracy (ACC), recall, precision, Dice similarity coefficient (DSC), and area under the curve (AUC). The results are 94.3%, 80%, 91.5%, 99%, and 96.7%, respectively. The comparisons with the existing built-in models, such as MobileNetV2, DenseNet201, SeResNext50, InceptionV3, and InceptionresNetv2, demonstrate the superiority of the proposed ML-CNN model.