Medical practitioners have great interest in getting the denoised signal before analysing it. EEG is widely used in detecting several neurological diseases such as epilepsy, narcolepsy, dementia, sleep apnea syndrome, Alzheimer's, insomnia, parasomnia, Creutzfeldt-Jakob diseases (CJD) and schizophrenia, etc. In the process of EEG recordings, a lot of background noise and other kind of physiological artefacts are present, hence, data is contaminated. Therefore, to analyse EEG properly, it is necessary to denoise it first. Total variation denoising is expressed as an optimisation problem. Solution of this problem is obtained by using a non-convex penalty (regulariser) in the total variation denoising. In this article, non-convex penalty is used for denoising the EEG signal. The result has been compared with wavelet methods. Signal to noise ratio (SNR) and root mean square error have been computed to measure the performance of the method. It has been observed that the approach used here works well in denoising the EEG signal and hence enhancing its quality.