The mechanisms and characteristics of the irregular variations of red supergiants (RSGs) are studied based on the RSG samples in the Small Magellanic Cloud (SMC), Large Magellanic Cloud (LMC), and M31. With the time-series data from the All-Sky Automated Survey for SuperNovae and Intermediate Palomar Transient Factory survey, we use the continuous time autoregressive moving average model to estimate the variability features of the light curves and their power spectral density (PSD). The characteristic evolution timescale and amplitude of granulations are further derived from fitting the posterior PSD with the COR function, which is a Harvey-like granulation model. The consistency of theoretical predictions and results is checked to verify the correctness of the assumption that granulations on RSGs contribute to irregular variation. The relations between granulation and stellar parameters are obtained and compared with the results of red giant branch (RGB) stars and Betelgeuse. It is found that the relations are in agreement with predictions from basic physical process of granulation and fall close to the extrapolated relations of RGB stars. The granulations in most of the RSGs evolve at a timescale of several days to a year with a characteristic amplitude of 10-1000mmag. The results imply that the irregular variations of RSGs can be attributed to the evolution of granulations. When comparing the results from the SMC, LMC, and M31, the timescale and amplitude of granulation seem to increase with metallicity. The analytical relations of the granulation parameters with stellar parameters are derived for the RSG sample of each galaxy.