Stress has an impact, not only on a person’s physical health, but also on the ability to perform at the workplace in daily life. The well-established relation between psychological stress and its pathogeneses highlights the need for detecting psychological stress early, in order to prevent disease advancement and to save human lives. Electroencephalography (EEG) signal recording tools are widely used to collect these psychological signals/brain rhythms in the form of electric waves. The aim of the current research was to apply automatic feature extraction to decomposed multichannel EEG recordings, in order to efficiently detect psychological stress. The traditional deep learning techniques, namely the convolution neural network (CNN), long short-term memory (LSTM), bidirectional long short-term memory (BiLSTM), gated recurrent unit (GRU) and recurrent neural network (RNN) models, have been frequently used for stress detection. A hybrid combination of these techniques may provide improved performance, and can handle long-term dependencies in non-linear brain signals. Therefore, this study proposed an integration of deep learning models, called DWT-based CNN, BiLSTM, and two layers of a GRU network, to extract features and classify stress levels. Discrete wavelet transform (DWT) analysis was used to remove the non-linearity and non-stationarity from multi-channel (14 channel) EEG recordings, and to decompose them into different frequency bands. The decomposed signals were utilized for automatic feature extraction using the CNN, and the stress levels were classified using BiLSTM and two layers of GRU. This study compared five combinations of the CNN, LSTM, BiLSTM, GRU and RNN models with the proposed model. The proposed hybrid model performed better in classification accuracy compared to the other models. Therefore, hybrid combinations are appropriate for the clinical intervention and prevention of mental and physical problems.