Electroencephalogram (EEG) has been widely used in diagnosing brain-related diseases, brain-computer interface applications, and user authentication and identification in security systems. Large EEG databases have been built and therefore, an effective EEG compression technique is necessary to reduce data for transmitting, processing and storing. In this paper, we propose an EEG lossy compression scheme in which EEG signals are undergoing a Wavelet Transform operation, followed by Quantisation and Thresholding, before being coded by Adaptive Arithmetic Coder. Our experiments are performed on a large set of EEG signals taken from two public databases and the results show that the proposed compression technique gives better performance than current techniques.