The curvature and the helicity of single-wall carbon nanotube (SWCNT) are the important factors which influence the adsorption behaviors of metal atoms inside and outside carbon tubes. However, it is difficult to investigate the separate effects of SWCNT helicity on the adsorption behaviors of metal atoms. In the present work, the armchair (6, 6), zigzag (10, 0), and chiral (8, 4) tubes with similar curvature are selected, then the Rh adsorption behaviors inside and outside the tubes are systematically investigated using the density functional theroy. Due to the different SWCNT helicities, the stable configurations of Rh atoms on tubes are different. The neighbor carbon atoms interacting with Rh atoms vary with tube helicity, therefore, the Rh adsorption energies for a similar configuration are also different. It indicates that the outer charge density of SWCNT is higher than the inner one. Different helicities lead to different charge density variations along the radial direction. Charge density difference shows that the orbital orientations of Rh adatom and the electrons obtained and lost are slightly different due to the different helicities. The bandstructure indicates that the doping band appears near the Fermi energy level. The (6, 6) tube with Rh adatom still exhibits metallicity. When Rh atoms are adsorbed inside the (10, 0) tube, the nanotube transforms from the semiconducting into the metallic one. However, the band gap reduces when Rh atoms adsorbed outside the tube. After the Rh adsorption, the (8, 4) tube band gap reduces.