The high-energy cosmic-ray electron spectrum between 9 and 300 GeV has been measured using an instrument consisting of a combination of a transition-radiation detector and a shower detector. The instrument has been calibrated at accelerators over the energy range 5-300 GeV and has been exposed in a balloon flight for 9.3 sq m sr hr. The design of the instrument and the data analysis procedures are described. It is found that the electron spectrum is significantly steeper than the proton spectrum. If the spectrum is fitted to a single power law, a spectral index of 3.35 is obtained. This suggests the influence of radiative energy losses on galactic electrons at low energies. The results are interpreted in the context of the homogeneous model for galactic cosmic rays.