CrI3 in two-dimensional (2D) forms has been attracting much attention lately due to its novel magnetic properties at atomic large scale. The size and edge tuning of electronic and magnetic properties for 2D materials has been a promising way to broaden or even enhance their utility, as the case with nanoribbons/nanotubes in graphene, black phosphorus, and transition metal dichalcogenides. Here we studied the CrI3 nanoribbon (NR) and nanotube (NT) systematically to seek the possible size and edge control of the electronic and magnetic properties. We find that ferromagnetic ordering is stable in all the NR and NT structures of interest. An enhancement of the Curie temperature TC can be expected when the structure goes to NR or NT from its 2D counterpart. The energy difference between the FM and AFM states can be even improved by up to 3–4 times in a zigzag nanoribbon (ZZNR), largely because of the electronic instability arising from a large density of states of iodine-5p orbitals at EF. In NT structures, shrinking the tube size harvests an enhancement of spin moment by up to 4％, due to the reduced crystal-field gap and the re-balance between the spin majority and minority populations.