The structural phase transition, elastic, electronic properties and hardness for boride rhodium (RhB) under high pressure are systematically investigated by using the pseudopotential plane-wave density functional. The obtained lattice parameters, bulk modulus and elasitc constants are in good agreement with the available experimental and previous theoretical results at zero pressure. Furthermore, the mechanism of the high pressure structural phase transition is studied in detail. Our results show that RhB undergoes a structural phase transition from anti-NiAs-type to FeB-type at 25.3 GPa, which is in good agreement with other reported theoretical result. We also predict the pressure induced elastic constants, bulk modulus, shear modulus, Young's modulus, Poisson's coefficients, and elastic anisotropy factors, and find that the pressure has an important influence on the elastic properties. The calculated electronic density of states reveals that the pressure will strengthen the orbital hybridization between the Rh states and B states, the nonlocal effect and the strength of the covalent bond. Finally, on the basis of the Mulliken overlap populationanalysis, we obtain that the hardness of anti-NiAs-RhB is 18.1 GPa, which is compatible to the experimental value.