The CALorimetric Electron Telescope (CALET) installed on the International Space Station has multiple event trigger modes for measuring high-energy particles and gamma rays. The observations of the low-energy cosmic-ray (CR) electrons (electrons + positrons) in an energy region from 1 GeV to 10 GeV have been successfully performed by a low-energy shower trigger mode working in the geomagnetic polar regions. The continuous measurements of the low-energy CR electrons may provide a crucial key to the understanding of the solar modulation of the galactic cosmic rays. Here we have analyzed the low-energy CR electrons measured by CALET over the past three years to investigate the solar modulation of the CR electrons. We have obtained the continuous variation of the low-energy electron flux increasing as time passes, which have been expected from a recent weakening solar cycle. We have also confirmed that there are additional small fluctuations in the flux, that has a potential to be explained by the effects of the interplanetary coronal mass ejections or the co-rotating interaction region of the solar wind.