X-ray spectra of back hole binaries are known to switch between the High/Soft state
(HSS) and the Low/Hard state (LHS) respectively when the mass accretion rate being
higher and lower. The spectra of both states can be approximated by two component:
direct thermal emission from optically-thick accretion disk and optically-thin
Comptonized emission.  The spectra in the HSS is dominated by the disk component, while
those in the LHS are dominated by the Compton component. The difference is due the
innermost radius of the disk, which is truncated for the LHS and reaches the innermost
circular orbit (ISCO) in the general-relativistic domain for the HSS. When the black
hole binaries evolve from the LHS to the HSS, they often go through another spectral
state called very high state (VHS). It is interesting to see whether the inner disk
radius reaches the ISCO and how the Compton component evolves during the VHS.

We report the results of Suzaku observations of the black hole binary LMC X-1 carried
out in 2009 from July 21 to 24. The time-averaged X-ray spectra are explained by a
multi-color disk and a combination of hard and soft Comptonized emission components,
which characterizes the VHS. By spectral fitting, we found a spectral variation that is
well attributable to the changes only in the hard Comptonized emission component. In
comparison to other black hole binaries, we propose a picture of the spectral evolution
in the VHS, in which the thermal Comptonizing cloud is cooled by an expansion of
optically-thick disk.