A spectrum of coherent synchrotron radiation emitted from a bunch train of relativistic electrons accelerated by the Tohoku 300-MeV linear accelerator (linac) has been observed in the wavelength range from 0.16 to 3.5 mm. The energy of the electrons and the longitudinal bunch length are 150 MeV and about 2 mm. The observed spectrum has a broad peak at lambda-congruent-to 1.5 mm, and the intensity decreases sharply towards shorter wavelengths. The peak intensity is enhanced by a factor of 5 x 10(6) in comparison with ordinary incoherent synchrotron radiation; the enhancement factor is comparable with the average number of electrons in the bunch. The electron distribution in the bunch is derived from the observed spectrum, and the bunch length (full width at half maximum) is obtained to be 0.25 mm. This bunch length is shorter than that estimated from the characteristics of the linac. The relation between the spectrum and the distribution of electrons in the bunch is discussed.