The characteristics of infrared properties and mid-infrared (MIR) variability of red supergiant (RSG) stars in the Large Magellanic Cloud (LMC) are analyzed based on 12 bands of near-infrared (NIR) to MIR co-added data from 2MASS, Spitzer and WISE, and ~6.6 years of MIR time-series data collected by the ALLWISE and NEOWISE-R projects. 773 RSGs candidates are compiled from the literature and verified by using the color-magnitude diagram (CMD), spectral energy distribution (SED) and MIR variability. About 15% of valid targets in the IRAC1-IRAC2/IRAC2-IRAC3 diagram may show Polycyclic Aromatic Hydrocarbon (PAH) emission. We show that arbitrary dereddening Q parameters related to the IRAC4, S9W, WISE3, WISE4 and MIPS24 bands could be constructed based on a precise measurement of MIR interstellar extinction law. Several peculiar outliers in our sample are discussed, in which one outlier might be a RSG right before the explosion or an extreme asymptotic giant branch (AGB) star in the very late evolutionary stage based on the MIR spectrum and photometry. There are 744 identified RSGs in the final sample having both the WISE1- and WISE2-band time-series data. The results show that the MIR variability is increasing along with the increasing of brightness. There is a relatively tight correlation between the MIR variability, mass loss rate (MLR; in terms of K_S-WISE3 color) and the warm dust/continuum (in terms of WISE4 magnitude/flux), where the MIR variability is evident for the targets with K_S-WISE3>1.0mag and WISE4<6.5mag, while the rest of the targets show much smaller MIR variability. The MIR variability is also correlated with the MLR for which targets with larger variability also show larger MLR with an approximate upper limit of -6.1M_{sun}_/yr. The variability and luminosity may both be important for the MLR since the WISE4-band flux is increasing exponentially along with the degeneracy of luminosity and variability. The identified RSG sample has been compared with the theoretical evolutionary models and shown that the discrepancy between observation and evolutionary models can be mitigated by considering both variability and extinction.