It is known that the mass distribution of the known neutron stars (NSs) exhibits a bimodal pattern. The origin of this distribution remains a subject of debate. We constructed a super-Eddington accretion model for accreting NSs and investigated the mass growth and distribution of these stars using the population synthesis method. We find, in our model, the mass growth of NSs depends on the binary orbital period and the mass of the donor star. Our results can successfully account for the bimodal distribution of NS masses. The peak distribution of NS masses at around ∼1.8 M⊙ primarily originates from NS binary systems where the donor star mass is less than ∼1.6 M⊙ and the orbital period is shorter than 20 days; meanwhile, NS systems may undergo common envelope evolution and these NSs can account for the mass peak at 1.4 M⊙.