The body-of-revolution, finite-difference time-domain (BOR-FDTD) method is presented for solving electromagnetic scattering from inhomogeneous dielectric BOR objects embedded in multilayered media. To efficiently truncate the infinite spatial domain for computations, a generalized unsplit perfectly matched layer (UPML) absorbing boundary condition technique in cylindrical coordinates is incorporated into the BOR-FDTD solver. The total-field scattered-field (TFSF) method is utilized to introduce the incident plane waves into the BOR-FDTD simulations. In the presence of the layered media, a 1-D auxiliary grid is created to generate a normal plane-wave injector by performing 1-D FDTD calculations along the direction of wave propagation with the help of a 1-D TFSF technique. The numerical results presented here demonstrate the accuracy and efficiency of the proposed method. Finally, the code is employed to investigate the influence of substrates on the characteristics of flat transformation optics (TO) BOR lenses.