A coherent scattering microscope for extreme ultraviolet (EUV) light has been developed for the actinic inspection of EUV lithography masks. It was installed at the NewSUBARU synchrotron facility. It provides aberration-free, diffraction-limited imaging and a high numerical aperture. Coherent EUV light scattered (diffracted) from a mask is recorded using an EUV charged coupled device camera with a numerical aperture of 0.15. An image of the sample is reconstructed using a hybrid input-output algorithm, which retrieves the phase from the intensity data. Masks containing periodic line-and-space and hole patterns with a half-pitch ranging from 100 to 400 nm were fabricated in the laboratory and imaged. The reconstructed images correlate well with images obtained with a scanning electron microscope (SEM). The actinic critical dimension of the linewidth of TaN absorber patterns on a mask was measured and was consistently found to be 25 nm larger than that obtained from the SEM data.