We demonstrate an alignment method for a laboratory-scale soft X-ray microscope, which utilizes a liquid-jet laser-produced plasma source in combination with a tandem ellipsoidal condenser mirror and a diffiractive micro zone plate. Because the intensity of the laser-produced plasma source is relatively low, we developed the tandem ellipsoidal condenser mirror to increase the photon density in the objective plane and to obtain a high-resolution image within a short exposure time. But, aligning the tandem ellipsoidal condenser mirror is a difficult task because it has 5 degrees of freedom (DOF) alignment tolerances and there is a connection among these tolerances. We performed its tolerance analysis and developed a new fully automated alignment algorithm via computer control. As a result, a 12.5-mu m-pitch gold mesh image was measured using 700x magnification and a 5 min exposure and the resultant edge detection resolution was about 70 nm.