Humans experience a variety of emotions throughout the course of their daily lives, including happiness, sadness, and rage. As a result, an effective emotion identification system is essential for electroencephalography (EEG) data to accurately reflect emotion in real-time. Although recent studies on this problem can provide acceptable performance measures, it is still not adequate for the implementation of a complete emotion recognition system. In this research work, we propose a new approach for an emotion recognition system, using multichannel EEG calculation with our developed entropy known as multivariate multiscale modified-distribution entropy (MM-mDistEn) which is combined with a model based on an artificial neural network (ANN) to attain a better outcome over existing methods. The proposed system has been tested with two different datasets and achieved better accuracy than existing methods. For the GAMEEMO dataset, we achieved an average accuracy ± standard deviation of 95.73% ± 0.67 for valence and 96.78% ± 0.25 for arousal. Moreover, the average accuracy percentage for the DEAP dataset reached 92.57% ± 1.51 in valence and 80.23% ± 1.83 in arousal.