  We compute gravitational waves emitted by the collapse of a rotating very
massive star (VMS) core leading directly to a black hole in axisymmetric
numerical-relativity simulations. The evolved rotating VMS is derived by a
stellar evolution calculation and its initial mass and the final carbon-oxygen
core mass are $320M_\odot$ and $\approx 150M_\odot$, respectively. We find that
for the moderately rapidly rotating cases, the peak strain amplitude and the
corresponding frequency of gravitational waves are $\sim 10^{-22}$ and $f
\approx 300$--600\,Hz for an event at the distance of $D=50$~Mpc. Such
gravitational waves will be detectable only for $D \lesssim 10$~Mpc by second
generation detectors, advanced LIGO, advanced VIRGO, and KAGRA, even if the
designed sensitivity for these detectors is achieved. However, third-generation
detectors will be able to detect such gravitational waves for an event up to $D
\sim 100$~Mpc. The detection of the gravitational-wave signal will provide a
potential opportunity for verifying the presence of VMSs with mass $\gtrsim
300M_\odot$ and their pair-unstable collapse in the universe.
