In the latest 20 years, x-ray imaging technology has developed fast in order to meet the need of x-ray photo-etching, spatial exploration technology, high-energy physics, procedure diagnosis of inertial confinement fusion (ICF) etc. But, Since refractive index of materials in the x-ray region is lower than 1, and x-ray is strongly absorbed by the materials, it is very difficult to image objects in the x ray region. Conventional imaging methods are hardly suitable to x-ray range. Generally, grazing reflective imaging and coding aperture imaging methods have been adopted more and more. In this paper, non-coaxial grazing reflective imaging KB and KBA microscope systems are discussed in detail, and an x-ray microscope consisting of four mirrors working at grazing incidence is designed. It is an anastigmatic system, and the oblique angle of the image is evidently decreased. The resolution of 5-7 can be obtained within 2 field of view. And finally we also make analysis of the key problems that are met in the processing of manufacturing this system are analyzed.