We report on a soft x-ray microscope using a gas-discharge plasma with pseudo spark-like electrode geometry as a light source. The source produces a radiant intensity of 4 x 10(13) photons/(sr pulse) for the 2.88 nm emission line of helium-like nitrogen. At a demonstrated 1 kHz repetition rate a brilliance of 4.3 x 10(9) photons/(microm2 sr s) is obtained for the 2.88 nm line. Ray-tracing simulations show that, employing an adequate grazing incidence collector, a photon flux of 1 x 10(7) photons/(microm2 s) can be achieved with the current source. The applicability of the presented pinch plasma concept to soft x-ray microscopy is demonstrated in a proof-of-principle experiment.