  It is proposed that one-off fast radio burst (FRB) with periodic structures
may be produced during the inspiral phase of a binary neutron-star (BNS)
merger. In this paper, we study the event rate of such kind of FRB. We first
investigate the properties of two one-off FRBs with periodic structures (i.e.,
FRB~20191221A and FRB~20210213A) in this scenario, by assuming the fast
magnetosonic wave is responsible for their radio emission. For the luminosities
and periods of these bursts, it is found that the pre-merger BNS with magnetic
field strength $B\gtrsim 10^{12}\,{\rm Gs}$ is required. This is relatively
high compared with that of the most of the BNSs observed in our Galaxy, of
which the magnetic field is around $10^{9}\,{\rm Gs}$. Since the observed BNSs
in our Galaxy are the binaries without suffering merger, a credited event rate
of BNS-merger originated FRBs should be estimated by considering the evolution
of both the BNS systems and their magnetic fields. Based on the population
synthesis and adopting a decaying magnetic field of NSs, we estimate the event
rate of BNS-mergers relative to their final magnetic fields. We find that the
rapid merged BNSs tend to merge with high magnetization, and the event rate of
BNS-merger originated FRBs, i.e., the BNS-mergers with both NSs' magnetic field
being higher than $10^{12}\,{\rm Gs}$ is $\sim8\times10^{4}\,\rm{yr}^{-1}$ ($19
\%$ of the total BNS-mergers) in redshift $z<1$.
