A steering apparatus of a vehicle includes a plurality of coupling portions formed in a rack housing of a gear box and coupled to mounting portions of a vehicle body; and a nut member having a support surface and installed in each of the mounting portions of the vehicle body. In particular, each of the plurality of coupling portions has a seating surface formed as a curved surface with a predetermined curvature, and the seating surfaces are respectively seated on the support surface of the nut member installed in each of the mounting portions of the vehicle body such that the rack housing of the gear box is fixed to the vehicle body by a bolt which passes through each of the plurality of coupling portions to be engaged with the nut member of each of the mounting portions.