Using first-principles calculations based on density functional theory and projector augmented wave method, we investigate the electronic structures of one-dimensional wurtzite (WZ) and zinc-blende (ZB) GaSb nanowires with different diameters along the 0001 and 111 directions, respectively. The results show that the band gap of the GaSb nanowire increases as the size of the nanowire decreases due to the quantum confinement, and the band structures of the GaSb nanowires display an indirect band structures feature when the diameter of the nanowire is smaller than 3.0 nm, whereas bulk GaSb has a direct gap. Owing to the different responses of the valence band maximum/conduction band minimum energies to strain, the band structures of GaSb nanowires experiences a noticeable indirect-to-direct transition when the nanowires are under the uniaxial strain. For example, an indirect-to-direct band gap transition in the band structure of 111 ZB GaSb nanowires can be realized by applying a uniaxial tensile strain, and this transition in the band structure of 0001 WZ GaSb nanowires can take place by applying both uniaxial tensile and compression strain when the diameter of the nanowire is about 2.0 nm. In addition, it is found that carrier effective mass is dependent on the diameter of the GaSb nanowire, therefore both the electron and hole effective mass values decrease as diameter increases. It is also found that the hole effective mass is smaller than the electron effective mass for GaSb nanowires with the same directions and sizes, indicating that the hole transportation is more prominent than the electron transportation.