Dyslexia is a learning disability in acquiring reading skills, even though the individual has the appropriate learning opportunity, adequate education, and appropriate sociocultural environment. Dyslexia negatively affects children's educational development; hence, early detection is highly important. Electrooculogram (EOG) signals are one of the most frequently used physiological signals in human-computer interfaces applications. EOG is a method based on the examination of the electrical potential of eye movements. The advantages of EOG-based systems are non-invasive, affordable, easy to record, and can be processed in real time. In this paper, a novel 1D CNN approach using EOG signals is proposed for the diagnosis of dyslexia. The proposed approach aims to diagnose dyslexia using EOG signals that are recorded simultaneously during reading texts, which are prepared in different typefaces and fonts. EOG signals were recorded from both horizontal and vertical channels, thus comparing the success of vertical and horizontal EOG signals in detecting dyslexia. The proposed approach provided an effective classification without requiring any hand-crafted feature extraction techniques. The proposed method achieved classifier accuracy of 98.70% and 80.94% for horizontal and vertical channel EOG signals, respectively. The results show that the EOG signals-based approach gives successful results for the diagnosis of dyslexia.