The objective of this study is to propose an alternative, hybrid solution method for diagnosing diabetic retinopathy from retinal fundus images. In detail, the hybrid method is based on using both image processing and deep learning for improved results. In medical image processing, reliable diabetic retinopathy detection from digital fundus images is known as an open problem and needs alternative solutions to be developed. In this context, manual interpretation of retinal fundus images requires the magnitude of work, expertise, and over-processing time. So, doctors need support from imaging and computer vision systems and the next step is widely associated with use of intelligent diagnosis systems. The solution method proposed in this study includes employment of image processing with histogram equalization, and the contrast limited adaptive histogram equalization techniques. Next, the diagnosis is performed by the classification of a convolutional neural network. The method was validated using 400 retinal fundus images within the MESSIDOR database, and average values for different performance evaluation parameters were obtained as accuracy 97%, sensitivity (recall) 94%, specificity 98%, precision 94%, FScore 94%, and GMean 95%. In addition to those results, a general comparison of with some previously carried out studies has also shown that the introduced method is efficient and successful enough at diagnosing diabetic retinopathy from retinal fundus images. By employing the related image processing techniques and deep learning for diagnosing diabetic retinopathy, the proposed method and the research results are valuable contributions to the associated literature.