It is necessary to remove the noise in EEG before further EEG analysis and processing. For EEG is deeply masked in the noise background, it is very difficult to denoise EEG effectively. Proposed in this paper is a novel realistic head model based sparse decomposition algorithm to denoise EEG, which is an iterative procedure combining the subject's physiology of EEG generation into the denoising procedure. In this algorithm, the lead field overcomplete dictionary is numerically calculated according to the realistic head model firstly, and then the instantaneous EEG spatial potential is decomposed into one sparse combination of atoms in the lead field matrix by matching pursuit, and the sparse combination of atoms is to be regarded as the denoised EEG signal. The realistic head based sparse decomposition was tested by the simulated noisy potential and a real EEG recording collected in an oddball stimulus experiment, the results consistently confirmed the new method removed the uncorrelated noise in EEG effectively.