  We derive the gravitational waveform from the collapse of a rapidly rotating
supermassive star (SMS) core leading directly to a seed of a supermassive black
hole (SMBH) in axisymmetric numerical-relativity simulations. We find that the
peak strain amplitude of gravitational waves emitted during the black-hole
formation is $\approx 5 \times 10^{-21}$ at the frequency $f \approx 5$\,mHz
for an event at the cosmological redshift $z=3$, if the collapsing SMS core is
in the hydrogen-burning phase. Such gravitational waves will be detectable by
space laser interferometric detectors like eLISA with signal-to-noise ratio
$\approx 10$, if the sensitivity is as high as LISA for $f=1$--10\,mHz. The
detection of the gravitational-wave signal will provide a potential opportunity
for testing the direct-collapse scenario for the formation of a seed of SMBHs.
