The properties of omnidirectional band gap (OBG) in the two-dimensional superconductor photonic crystals (SPCs) with triangular lattices, that are composed of the superconductor (Nb) rods in the dielectric background, are theoretically studied in detail based on the modified plane wave expansion method, as the electromagnetic wave with a off-plane angle. The calculated results demonstrate that not only the complete photonic band gap (PBG) and a flatbands region can be achieved but also the OBG can be observed. The influences of the radius of inserted rod, the dielectric background, the plasma frequency of superconductor, the damping coefficient of the superconductor, and the ambient temperature on the OBG are investigated, respectively. The simulations show that the tunable OBG can be obtained except for changing the damping coefficient of the superconductor. The features of OBG for the complementary structure also are discussed as the anisotropic materials are introduced. The analysis results show that the complete PBG also can be achieved in the large incidence angle region. These values provide the theoretical instructions to realize the omnidirectional reflector by the proposed SPCs.