The structural, electronic, mechanical, and vibrational properties of 4d transition metal mononitride, RhN, are investigated using the norm-conserving pseudopotentials within the local density approximation (LDA) in the frame of density functional theory. The calculated lattice parameters and the bulk modulus almost agree with the previous theoretical values. The second-order elastic constants have been calculated and the other related quantities such as Young's modulus, shear modulus, anisotropy factor, sound velocities, and Debye temperature also estimated. Charge distributions and density of states are reported to understand the bonding character in the stable phases. We have also obtained the phonon dispersion curves without LO/TO splitting.