We study the formation of lenses of the ocean's intermediate water using a 2.5-layerβ-plane primitive equation model with localized injection of water mass. For the injecting rate of 1.0 Sv, we have observed that strong vortices are shed regularly. These vortices propagate westward much faster than the second baroclinic long Rossby wave. They are totally isolated from each other and show strong baroclinicity as well. Moreover, they remain stable over a sufficiently long period of time. Regular formation of such strong vortices in the intermediate layer has not been reported previously. The translation speed is explained using the Euler's momentum integral theorem for the nonlinear baroclinic vortex on the β-plane. We have demonstrated that coupling between the primary motion in the intermediate layer and the secondary motion in the upper layer with a meridional shift is crucial to the fast westward translation of the intense vortices. A simple dispersion formula relating the zonal translation speed with the vortex radius is also derived under the assumption of quasi-geostrophy. It has turned out that the analytical relation explains the numerical results surprisingly well despite the limitation of its derivation.