Epileptic seizures are among the most significant chronic neurological disorders, caused by abnormal electrical activity in the brain and accompanied by symptoms such as limb tremors, loss of consciousness, and speech disturbances. Electroencephalography (EEG) is considered one of the most important tools for diagnosing epileptic seizures due to its non-invasiveness and relatively low cost; however, it faces challenges such as artifacts and low spatial resolution. In this study, a computer-aided diagnosis system (CADS) is proposed for the detection of epileptic seizures. For this purpose, the Turkish epilepsy dataset was used for experiments. In the first step, standard preprocessing procedures were applied to the EEG signals. Then, handcrafted features were extracted from the EEG channels to provide a compact representation of the local dynamics of the signals. Next, a brain graph was constructed using an adjacency matrix based on the Pearson correlation method and was used as input to the proposed deep learning (DL) architecture. Finally, a proposed graph convolutional network (GCN) was employed to extract discriminative features from the preprocessed EEG signals. The results show that the proposed method achieved a maximum accuracy (Acc) of 95.72% using EEG signals with a 15-s time frame.