Mass loss is an important activity for red supergiants (RSGs) and can influence their evolution and final fate. Previous estimations of mass-loss rates (MLRs) of RSGs exhibit significant dispersion due to differences in method and the incompleteness of samples. With the improved quality and depth of surveys including the UKIRT/WFCAM observations in the near-infrared, and LGGS and PS1 in the optical, a rather complete sample of RSGs is identified in M31 and M33 according to their brightness and colors. For about 2000 objects in either galaxy from this largest ever sample, the MLR is derived by fitting the observational optical-to-mid-infrared spectral energy distribution with the DUSTY code of a 1D dust radiative transfer model. The average MLR of RSGs is found to be around 2E-5 solar mass per year with a gas-to-dust ratio of 100, which yields a total contribution to the interstellar dust from RSGs of about 1.1E-3 solar mass per year in M31 and 6E-4 in M33, a non-negligible source in comparison with evolved low-mass stars. The MLRs are divided into three types by the dust properties, i.e., amorphous silicate, amorphous carbon, and optically thin, and the relations between MLR and stellar parameters, infrared flux, and colors are discussed and compared with previous works for the silicate and carbon dust groups.