In recent years, advanced neurocomputing and machine learning techniques have been used for Electroencephalogram (EEG)-based diagnosis of various neurological disorders. In this paper, a novel computer model is presented for EEG-based screening of depression using a deep neural network machine learning approach, known as Convolutional Neural Network (CNN). The proposed technique does not require a semi-manually-selected set of features to be fed into a classifier for classification. It learns automatically and adaptively from the input EEG signals to differentiate EEGs obtained from depressive and normal subjects. The model was tested using EEGs obtained from 15 normal and 15 depressed patients. The algorithm attained accuracies of 93.5% and 96.0% using EEG signals from the left and right hemisphere, respectively. It was discovered in this research that the EEG signals from the right hemisphere are more distinctive in depression than those from the left hemisphere. This discovery is consistent with recent research and revelation that the depression is associated with a hyperactive right hemisphere. An exciting extension of this research would be diagnosis of different stages and severity of depression and development of a Depression Severity Index (DSI).