The frequency-dependent periodic active window of the fast radio burst FRB 180916.J0158+65 (FRB 180916B) was observed recently. In this Letter, we propose that a Be/X-ray binary (BeXRB) system, which is composed of a neutron star (NS) and a Be star with a circumstellar disk, might be the source of a repeating FRB with periodic activities, and apply this model to explain the activity window of FRB 180916B. The interaction between the NS magnetosphere and the accreted material results in evolution of the spin period and the centrifugal force of the NS, leading to the change of the stress in the NS crust. When the stress of the crust reaches the critical value, a starquake occurs and further produces FRBs. The interval between starquakes is estimated to be a few days that is smaller than the active window of FRB 180916B. When the NS moves out of the disk of the Be star, the interval between starquakes becomes much longer than the orbital period, which corresponds to the non-active phase. In this model, due to the absorption of the disk of the Be star, a frequency-dependent active window would appear for the FRBs, which is consistent with the observed properties of FRB 180916B. And the contribution of dispersion measure (DM) from the disk of the Be star is small. In addition, the location of FRB 180916B in the host galaxy is consistent with a BeXRB system.
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