Using ab initio hybrid density functional theory based calculations, we report here the electronic and geometric structure properties of three different types of single-walled zigzag silicon carbide nanotube simulated by finite clusters with dangling bonds saturated by hydrogen atoms. These three types differ in the spatial arrangements of Si and C atoms. Full geometry and spin optimizations have been performed without any symmetry constraints. A detailed comparison of the structures and stabilities of the three types of nanotube is presented. Our calculations show type 1 structures to be more stable than type 2 structures, consistent with another result found in the literature. The cohesive energies/atom of the newly proposed type 3 nanotubes lie in between type 1 and type 2. The dependence of the electronic band gaps on the respective tube diameters, energy density of states and dipole moments as well as Mulliken charge distributions have been investigated. For all types of nanotube, Si atoms moved outward of the tube axis making two concentric cylinders of Si and C atoms after relaxation, contrary to some published results in the literature for type 1 zigzag nanotubes. The band gaps for type 1 and type 2 nanotubes show an oscillatory pattern as the diameter increases. Unlike the other two types, the band gap for type 3 nanotubes decreases monotonically with increasing tube diameter. All the tubes studied here appear to have triplet ground states except for type 1 (3, 0). It is expected that these tubes with significant surface reconstructions, varieties of band gaps, and magnetic properties would have interesting and important applications in the field of band gap engineering and molecular electronics.