Superhalogen anions are characterized by a higher vertical detachment energy (VDE) than those of halides. Ammonium borohydride, [NH4+][BH4-], is a potential candidate for high-capacity hydrogen storage but is not practically used due to its instability against dissociation to ammonia borane. Interestingly, BH4- is a superhalogen anion, and therefore, we use polynuclear BxH3x+1- superhalogen anions and study [NH4+][BxH3x+1-] complexes for x = 2-5 using density functional theory. The gravimetric hydrogen density of these complexes is smaller than that of [NH4+][BH4-] only slightly. We calculate the dehydrogenation energy and the Gibbs free energy of [NH4+][BxH3x+1-] complexes through ammonia borane. We notice that these complexes are more stable than [NH4+][BH4-], whose stability increases with an increase in x. The enhanced stability of [NH4+][BxH3x+1-] complexes appears as a consequence of the increase in the VDE of polynuclear BxH3x+1- superhalogen anions. We believe that these findings might attract experimentalists to synthesize these complexes.