The numerical prediction of the effective mechanical properties of the reinforced braid inserted in automobile power steering hose is addressed. The key role of the reinforced braid layer is to suppress the excessive radial expansion of the hose subject to high pressure and temperature. The reinforced braid layer is in the structure composed of wrap and fill tows inclined to each with the specific helix angle. In order to predict the effective mechanical properties, we construct a 3-D finite element model of the unit cell (or RVE) of the reinforced braid in a periodic pattern, in which the detailed geometry of individual fiber tows is fully modeled. By making use of the superposition method and the 3-D finite element analysis, the effective mechanical properties are predicted. Numerical experiments illustrating the theoretical work are also presented.