From previous samples of Red Supergiants (RSGs) by various groups, 191 objects are assembled to compose a large sample of RSG candidates in LMC. For 189 of them, the identity as a RSG is verified by their brightness and color indexes in several near- and mid-infrared bands related to the 2MASS JHKs bands and the Spitzer/IRAC and Spitzer/MIPS bands. From the visual time-series photometric observations by the ASAS and MACHO projects which cover nearly 8-10 years, the period and amplitude of light variation are analyzed carefully using both the PDM and Period04 methods. According to the properties of light variation, these objects are classified into five categories: (1) 20 objects are saturated in photometry or located in crowded stellar field with poor photometric results, (2) 35 objects with too complex variation to have any certain period, (3) 23 objects with irregular variation, (4) 16 objects with semi-regular variation, and (5) 95 objects with Long Secondary Period (LSP) among which 31 have distinguishable short period, and 51 have a long period shorter than 3000 days that can be determined with reasonable accuracy. For the semi-regular variables and the LSP variables with distinguishable short period, the period-luminosity relation is analyzed in the visual, near-infrared and mid-infrared bands. It is found that the P-L relation is tight in the infrared bands such as the 2MASS JHKs bands and the Spitzer/IRAC bands, in particular in the Spitzer/IRAC [3.6] and [4.5] bands; meanwhile, the P-L relation is relatively sparse in the V band which may be caused by the inhomogeneous interstellar extinction. The results are compared with others P-L relationships for RSGs and the P-L sequences of red giants in LMC.
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