Single-crystalline alpha-Fe2O3 nanorings (short nanotubes) and nanotubes were synthesized by a hydrothermal method. High-resolution transmission electron microscope and selected-area electron diffraction confirm that the axial directions of both nanorings and nanotubes are parallel to the crystalline c-axis. What is intriguing is that the Morin transition occurs at about 210 K in the short nanotubes with a mean tube length of about 115 nm and a mean outer diameter of 169 nm while it disappears in the nanotubes with a mean tube length of about 317 nm and a mean outer diameter of 148 nm. Detailed analyses of magnetization data, x-ray diffraction spectra, and room-temperature Mossbauer spectra demonstrate that this very strong shape dependence of the Morin transition is intrinsic to hematite. We can quantitatively explain this intriguing shape dependence in terms of opposite signs of the surface magnetic anisotropy constants in the surface planes parallel and perpendicular to the c-axis (that is, K_parallel = -0.37 erg/cm^2 and K_perp = 0.42 erg/cm^{2}).