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We present a design of a compact transmission water-window microscope based on the Z-pinching capillary discharge nitrogen plasma source. The microscope operates at wavelength of 2.88 nm (430 eV), and with its table-top dimensions provides an alternative to large-scale soft X-ray (SXR) microscope systems based on synchrotrons and free-electron lasers. The emitted soft X-ray radiation is filtered by a titanium foil and focused by an ellipsoidal condenser mirror into the sample plane. A Fresnel zone plate was used to create a transmission image of the sample onto a charge-coupled device (CCD) camera. To assess the resolution of the microscope, we imaged a standard sample-copper mesh. The spatial resolution of the microscope is 75 nm at half-pitch, calculated via a 10–90% intensity knife-edge test. The applicability of the microscope is demonstrated by the imaging of green algae-<i>Desmodesmus communis</i>. This paper describes the principle of capillary discharge source, design of the microscope, and experimental imaging results of Cu mesh and biological sample.