New projection-type X-ray microscope with a compound refractive lens as the optical element is presented. The microscope consists of an X-ray source that is 1-2 mm in diameter, compound X-ray lens and X-ray camera that are placed in-line to satisfy the lens formula. The lens forms an image of the X-ray source at camera sensitive plate. An object is placed between the X-ray source and the lens as close as possible to the source, and the camera shows a shadow image of the object. Spatial resolution of the microscope depends on the lens focal length, lens aperture and the distance from the source to the object. One to two micron resolution may be achieved by placing the object at a distance of 1-5 mm from the source. The X-ray source may be designed with the target deposited on a 200-µm thick Be window, which permits the object to be placed very close to the emitting surface. The tube focal spot is equal to 1-2 mm. Results of imaging experiments with an ordinary copper anode X-ray tube and a 10-cm focal length spherical compound refractive X-ray lens are discussed.