We have developed a beam profile monitor using two Fresnel zone plates (FZPs) at the KEK-ATF (Accelerator Test Facility) damping ring to measure small electron-beam sizes for low-emittance synchrotron radiation sources. The monitor has a structure of an X-ray microscope, where two FZPs constitute an X-ray imaging optics. In the monitor system, the synchrotron radiation from the electron beam at the bending magnet is monochromatized to 3.235-keV X-rays by a crystal monochromator and the transverse electron-beam image is twenty-times magnified by the two FZPs and detected on an X-ray CCD camera. This monitor has the following advantages: (1) high spatial resolution, (2) non-destructive measurement, (3) real-time monitoring and (4) direct electron-beam imaging. With the beam profile monitor, we have succeeded in obtaining a clear electron-beam image and measuring the extremely small beam size less than 10 μm. The measured magnification of the imaging optics was in good agreement with the design value.