<p>In order to reduce memory usage and improve efficiency, the unconditionally stable locally 1-D (LOD)-FDTD method for bodies of revolution (BOR) is extended to Debye dispersive media based on the bilinear <em>Z</em> transform (BZT) theory. The LOD-BOR-FDTD method is proposed. To validate the Higher efficiency and Lower memory usage of the proposed algorithm, two numerical examples are given. Compared with the 3-D FDTD and ADI-BOR-FDTD result, they show good agreement and at least 80% of computational time to the ADI counterparts.</p>