The electroencephalogram (EEG) has great attraction in emotion recognition studies due to its resistance to deceptive actions of humans. This is one of the most significant advantages of brain signals in comparison to visual or speech signals in the emotion recognition context. A major challenge in EEG-based emotion recognition is that EEG recordings exhibit varying distributions for different people as well as for the same person at different time instances. This nonstationary nature of EEG limits the accuracy of it when subject independency is the priority. The aim of this study is to increase the subject-independent recognition accuracy by exploiting pretrained state-of-the-art Convolutional Neural Network (CNN) architectures. Unlike similar studies that extract spectral band power features from the EEG readings, raw EEG data is used in our study after applying windowing, pre-adjustments and normalization. Removing manual feature extraction from the training system overcomes the risk of eliminating hidden features in the raw data and helps leverage the deep neural network’s power in uncovering unknown features. To improve the classification accuracy further, a median filter is used to eliminate the false detections along a prediction interval of emotions. This method yields a mean cross-subject accuracy of 86.56% and 78.34% on the Shanghai Jiao Tong University Emotion EEG Dataset (SEED) for two and three emotion classes, respectively. It also yields a mean cross-subject accuracy of 72.81% on the Database for Emotion Analysis using Physiological Signals (DEAP) and 81.8% on the Loughborough University Multimodal Emotion Dataset (LUMED) for two emotion classes. Furthermore, the recognition model that has been trained using the SEED dataset was tested with the DEAP dataset, which yields a mean prediction accuracy of 58.1% across all subjects and emotion classes. Results show that in terms of classification accuracy, the proposed approach is superior to, or on par with, the reference subject-independent EEG emotion recognition studies identified in literature and has limited complexity due to the elimination of the need for feature extraction.