A four-channel multilayer Kirkpatrick-Baez (KB) microscope is developed for the 8-keV X-ray imaging of experiments on laser inertial confinement fusion (ICF). A periodic multilayer that works at 8 keV and with a grazing incidence angle of 1.0o is coated on reflective surfaces to achieve a spatial resolution higher than 5 \mu m and an effective solid angle higher than ~10-7 sr. A precise assembly is realized by a conical reference cone to couple with an X-ray framing camera. This study provides detailed information on an optical and multilayer design, assembly method, and experimental results with a Cu X-ray tube. The instrument provides a high-resolution and high-throughput X-ray image for backlit or self-emission imaging of laser plasma at Cu K\alpha line radiation in Shenguang series laser facilities.