This paper reports the results of Suzaku observation of the spectral variation of the black hole binary LMCX-1 in the soft state. The observation was carried out in 2009 from July 21 to 24. the obtained net count rate was similar to 30 counts s(-1) in the 0.5-50 keV band with similar to 10% peak-to-peak flux variation. The time-averaged X-ray spectrum cannot be described by a multi-color disk and single Compton component with its reflection, but requires additional Comptonized emissions. This double Compton component model allows a slightly larger inner radius of the multi-color disk, implying a lower spin parameter. Significant spectral evolution was observed above 8 keV along with a flux decrease on a timescale of similar to 10(4)-10(5) s. By spectral fitting, we show that this behavior is well explained by changes in the hard Comptonized emission component in contrast to the maintained disk and soft Comptonized emission.