Structures of zwitterionic micelles of 61 sulfobetaine SB3-14, CH3(CH2)(13)[N+(CH3)(2)](CH2)(SO3-)-S-3, molecules in water and in 0.15 and 0.015 mol L-1 NaX (X = F-, Br-, I-, and ClO4-) aqueous solutions were investigated by atomistic molecular dynamics simulations. The micelle presents a near-spherical shape and an average angle of 110 degrees between the zwitterionic headgroup and the alkyl tail that provides an L-type shape for the surfactants and exposes the positive charged ammonium groups to the solution. This allows anions to adsorb at the surface of the micelle and the amount of adsorbed anions follows the Hofrneister series F- < Cl- < Br- < I- < ClO4-, which directly correlates to the measured values of the zeta-potential. The size and shape of the micelle are not affected by the salt, except the solvent accessible surface area that decreases for strongly adsorbing anions such as ClO4- due to the approximation of the headgroups between adjacent surfactants. Indeed, the ion distribution shows the formation of ion-pair-type species between ammonium and perchlorate, which indicates that the adsorption is directly related to the easiness of the anion to partially lose its hydration shell.