The Electroencephalography (EEG) signals that indicate the electrical activity of the brain are acquired with a high sampling rate. Consequently, the size of the recorded EEG data is large. For storing and transmitting these data, large space and bandwidth are demanded. Therefore, preprocessing and compressing EEG data are important for efficient data transmission and storage. The purpose of this approach is to design an efficient EEG data compression system in terms of time and space complexities. The proposed system consists of three main units: preprocessing unit, compression unit, and reconstruction unit. The core of the compression process occurs in the compression unit. Different combinations of hybrid lossy/lossless compression techniques were tried in the compression process. In this study, both the Discrete Cosine Transform and the Discrete Wavelet Transform techniques were experimented for the lossy compression algorithm. The Arithmetic Coding and the Run Length Encoding were experimented then for the lossless compression algorithm. The final results showed that combining both the Discrete Cosine Transform and the Run Length Encoding yields the most optimal system complexity and compression ratio. This approach achieved up to CR = 94% at RMSE = 0:188.