  In the population synthesis simulations of Pop III stars, many BH (Black
Hole)-BH binaries with merger time less than the age of the Universe
$(\tau_{\rm H})$ are formed, while NS (Neutron Star)-BH binaries are not. The
reason is that Pop III stars have no metal so that no mass loss is expected.
Then, in the final supernova explosion to NS, much mass is lost so that the
semi major axis becomes too large for Pop III NS-BH binaries to merge within
$\tau_{\rm H}$. However it is almost established that the kick velocity of the
order of $200-500{\rm~ km~s^{-1}}$ exists for NS from the observation of the
proper motion of the pulsar. Therefore, the semi major axis of the half of
NS-BH binaries can be smaller than that of the previous argument for Pop III
NS-BH binaries to decrease the merging time. We perform population synthesis
Monte Carlo simulations of Pop III NS-BH binaries including the kick of NS and
find that the event rate of Pop III NS-BH merger rate is $\sim 1 {\rm Gpc^{-3}
yr^{-1}}$. This suggests that there is a good chance of the detection of Pop
III NS-BH mergers in O2 of Advanced LIGO and Advanced Virgo from this autumn.
