How to localize the neural electric activities within brain effectively and precisely from the scalp electroencephalogram (EEG) recordings is a critical issue for current study in clinical neurology and cognitive neuroscience. In this paper, based on the charge source model and the iterative re-weighted strategy, proposed is a new maximum neighbor weight based iterative sparse source imaging method, termed as CMOSS (Charge source model based Maximum neighbOr weight Sparse Solution). Different from the weight used in focal underdetermined system solver (FOCUSS) where the weight for each point in the discrete solution space is independently updated in iterations, the new designed weight for each point in each iteration is determined by the source solution of the last iteration at both the point and its neighbors. Using such a new weight, the next iteration may have a bigger chance to rectify the local source location bias existed in the previous iteration solution. The simulation studies with comparison to FOCUSS and LORETA for various source configurations were conducted on a realistic 3-shell head model, and the results confirmed the validation of CMOSS for sparse EEG source localization. Finally, CMOSS was applied to localize sources elicited in a visual stimuli experiment, and the result was consistent with those source areas involved in visual processing reported in previous studies.