We have performed high-resolution synthesis observations of the ¹²CO (J = 1-0) line emission from the radio lobe edge-on spiral galaxy NGC 3079 using a seven-element millimeter-wave interferometer at the Nobeyama Radio Observatory, which consisted of the 45 m telescope and six-element array. The nuclear molecular disk (NMD) of 750 pc radius is found to be inclined by 20° from the optical disk, and the NMD has spiral arms. An ultra-high-density core (UHC) of molecular gas was found at the nucleus. The gaseous mass of the UHC within 125 pc radius is as large as ~3 × 10⁸ M, an order of magnitude more massive than that in the same area of the Galactic center, and the mean density is as high as ~3 × 10³H₂ cm^-3. A position-velocity diagram along the major axis indicates that the rotation curve already starts at a finite velocity exceeding 300 km s^-1 from the nucleus. The surface mass density in the central region is estimated to be as high as ~10⁵ M pc^-2, producing a very deep gravitational potential. We argue that the very large differential rotation in such a deep potential will keep the UHC gravitationally stable during the current star formation.