There is a remarkable correlation between the spin periods of the accreting neutron stars in Be/X-ray binaries (BeXBs) and their orbital periods . Recently Knigge et al. (2011) showed that the distribution of the spin periods contains two distinct subpopulations peaked at $sim 10$ s and $sim 200$ s respectively, and suggested that they may be related to two types of supernovae for the formation of the neutron stars, i.e., core-collapse and electron-capture supernovae. Here we propose that the bimodal spin period distribution is likely to be ascribed to different accretion modes of the neutron stars in BeXBs. When the neutron star tends to capture material from the warped, outer part of the Be star disk and experiences giant outbursts, a radiatively-cooling dominated disk is formed around the neutron star, which spins up the neutron star, and is responsible for the short period subpopulation. In BeXBs that are dominated by normal outbursts or persistent, the accretion flow is advection-dominated or quasi-spherical. The spin-up process is accordingly inefficient, leading to longer periods of the neuron stars. The potential relation between the subpopulations and the supernova mechanisms is also discussed.
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