The presence of salt has a profound effect on the size, shape and structure of sodium dodecyl sulfate (SDS) micelles. There have been a great number of experiments on SDS micelles in the presence and absence of salt to study this complex problem. Unfortunately, it is not clear yet how electrolyte ions influence the structure of micelles. By describing the compromise between dominant mechanisms, a simplified atomic model of SDS in presence of salt has been developed and the molecular dynamics (MD) simulations of two series of systems with different concentrations of salt and charges of ion have been performed. Polydispersity of micelle size is founded at relatively high concentration of SDS and low charge of cation. Although the counter-ion pairs with head groups are formed, the transition of micelle shape is not observed because the charge of cation is not enough to neutralize the polar of micelle surface.