We have developed an advanced Kirkpartrick-Baez (AKB) x-ray microscope to diagnose laser-produced plasmas. The AKB microscope is composed of two pairs of hyperbolic and elliptic mirrors to avoid spherical aberration and field obliquity. The spatial response of the microscope has been measured by x-ray backlighting a fine grid with laser-plasma x rays. A spatial resolution of better than 3 microm has been obtained with 2.5-keV x rays over the field of 800 microm at a magnification of 25. This microscope has been applied for laser implosion experiments, resulting in high-resolution images of the compressed cores.