Provided is a carbon-fiber nonwoven cloth with low resistance to gases or liquids passing through, and low resistance in the thickness direction to heat or electricity, which is particularly appropriate for a gas diffusion electrode of a polymer electrolyte fuel cell; the cloth having an air gap with a diameter of at least 20 μm, at least some of the carbon fibers being continuous from one surface to the other surface, and the apparent density being 0.2-1.0 g/cm3, or, having an air gap with a diameter of at least 20 μm and at least some of the carbon fibers being mutually interlaced, and further, at least some of the carbon fibers being oriented toward the thickness direction and the apparent density being 0.2-1.0 g/cm3.