How to localize the neural electric activities effectively and precisely from the scalp EEG recordings is a critical issue for clinical neurology and cognitive neuroscience. In this paper, based on the spatial sparse assumption of brain activities, proposed is a novel iterative EEG source imaging algorithm, Lp norm iterative sparse solution (LPISS). In LPISS, the lp (p < or =1) norm constraint for sparse solution is integrated into the iterative weighted minimum norm solution of the underdetermined EEG inverse problem, and it is the constraint and the iteratively renewed weight that forces the inverse problem to converge to a sparse solution effectively. The conducted simulation studies with comparison to LORETA and FOCUSS for various dipoles configurations confirmed the validation of LPISS for sparse EEG source localization. Finally, LPISS was applied to a real evoked potential collected in a study of inhibition of return (IOR), and the result was consistent with the previously suggested activated areas involved in an IOR process.