A new simple method to measure the transverse beam spot size in the nanometer range is proposed for a beam diagnostic system at the collision point in future TeV region e+e- linear colliders. A high energy electron beam is injected at a right angle into a photon target of intense laser light, and generates high energy gamma-rays by Compton scattering. Since the laser light is stored inside a cavity resonator and forms a standing wave, the gamma-ray flux shows periodic variation with the period of the optical wavelength by scanning the electron beam trajectory along the laser beam axis. From this modulation depth, the transverse size of the electron beam can be easily determined by a simple relation. Using the Nd:YAG laser at wavelength 1.06-mu-m or 532 nm, we can measure the beam spot size of 60 nm in the FFTB experiment [9] with sufficient accuracy. The required laser peak power is about 20 MW to generate 1000 gamma-rays per bunch. If we employ a shorter wavelength laser, for example Ar2 excimer laser at the wavelength of 126 nm, it will be possible to measure the beam size down to 5 nm, which is almost close to the required beam size in future linear colliders in the TeV region.
