The first-principles were employed investigate the structure properties, elastic constant and electronic structure of two phases of the RuB2 (orthorhombic and hexagonal phase). The lattice parameter and volume of the two RuB2 phases are in good agreement with experimental values. The calculated elastic constants indicate that the RuB2 exhibits excellent mechanical properties. The electronic structure shows that hybridization occurs between Ru (d states) and B (p states) and form Ru-B covalent bonding forms. The results reveal that the hexagonal RuB2 is a stable phase at ground state