Edge effects on possible magnetism appearing in finite hydrogenated zigzag nanotubes are investigated using the DFT-LSDA calculations. Our result shows that two types of edges, i.e. a mono-hydrogenated zigzag edge (MHZE) and a di-hydrogenated zigzag edge (DHZE), can give magnetic moments in finite nanotubes. Due to curvature of the tube, however, the total magnetic moment Stot is smaller than an expected value given by a counting rule of 5tot, which holds for magnetic nanographite ribbons. In addition to magnetic nanotubes found by Okada and Oshiyama, we show that a (7, 0) tube and an (8,0) tube with both MHZE and DHZE are magnetic. The reactions to create hydrogenated (7,0) and (8,0) tubes are exothermic.