The coherent effect in spontaneous emission has been observed in a low-energy, low-gain, waveguidemode free-electron laser. The intensity of the radiation was more than 10 3 times stronger than that of the incoherent radiation. This enhancement is due to coherent radiation emitted by the electron beam which is randomly modulated by micropulses whose typical pulse width ( -35 ps) is comparable to the radiation wavelength. The measured power tends towards a quadratic dependence on the electron-beam current. PACS numbers: 4l.60.Cr, Relativistic electrons passing through a magnetic undulator are subject to transverse acceleration, which results in emission of spontaneous radiation. The amount and spectrum of this radiation is a crucial factor in the startup process of the free-electron-laser (FEL) oscillator. This radiation has been used as a light source in many fields and also as a diagnostic tool for the electron beam.After the radiation emitted by a wiggling particle was first discussed analytically [1], theoretical [2-12] and experimental [13][14][15] investigation of this radiation was carried out by several authors. Nodvick and Saxon [16] predicted coherent synchrotron radiation from an electron beam with a bunch length comparable to the radiation wavelength. Recently the coherent effect in synchrotron radiation from a bending magnet [17] and in Cherenkov radiation [18] has been observed in a wavelength region comparable to the longitudinal electron bunch length. Even though the coherent effect in the undulator is expected [1,3], there has been no report of an observation of coherent undulator radiation. It is very difficult to generate a short electron beam whose bunch length is comparable to the wavelength of radiation in the visible or ir region. We have developed a laser-irradiated photocathode for a millimeter-wavelength-range FEL; hence our system is adequate to carry out experiments on coherent undulator radiation.In this paper, we report on the observation of the coherent effect in spontaneous emission. Intense radiation power, which was more than 10 3 times stronger than the power of incoherent radiation, was observed. This enhancement is caused by the coherent radiation of electron-beam micropulses (pulse width -35 ps), which have a slightly longer pulse duration than the emitted radiation wavelength. The measured radiation power tends towards a quadratic dependence on the electron-beam current. It was confirmed experimentally that the enhancement of the radiation power was caused by the electron-beam micropulses.The radiation power emitted by electrons passing through the undulator can be obtained by using Nodvick and Saxon's analytical consideration [16]. The total power P ( radiated by TV electrons iswhere