We have performed high-energy electron observations using balloon-borne emulsion chambers, and derived the cosmic-ray electron spectrum in the energy range from 30 GeV to 3 TeV. For the calibration of the emulsion chambers, we have also carried out beam tests of 50 GeV, 200 GeV, and 250 GeV electrons at CERN-SPS. The Landau-Pomeranchuk-Migdal (LPM) effect predicts the reduction of amplitude for bremsstrahlung photon emission. It affects to the depth of the first electron-positron pair of the electron-induced shower, the so-called shower starting point. In the emulsion chambers, we can measure the shower starting points for high-energy electrons with the position resolution of 1 µm. From the observations of accelerator-beam electrons of 200 GeV and 250 GeV, and cosmic-ray electrons above 400 GeV, we found the direct evidence of suppression of the bremsstrahlung cross sections due to the LPM effect.