Provided are napped fabrics with naps comprising a tapered fiber of a sheath-core polyester fiber with the sheath component having larger alkali hydrolysis rate than the core component, the core of the tapered fiber being exposed at its end part and having smooth surface, the sheath of at least the tapered part having minutely roughened surface. The napped fabrics are of high quality, having good hand and excellent color developing property without unnatural luster such as dark fading or white appearance and being difficult to soil, and are hence markedly suited for car seat cover.