Isotropic NMR shielding constants σ_iso were calculated for hydrogen, carbon, nitrogen, oxygen, fluorine and phosphorous atoms in small molecules by using numerical basis functions, which were based on AOs of Discrete Variational Xα (DV-Xα) method and were modified to London atomic orbitals to avoid the gauge-origin-dependence when magnetic field exists. In DV-Xα method AOs are prepared by solving the Hartree-Fock-Slater (HFS) equation substantially equivalent to that used to calculate MOs and are very accurate around each nucleus. However, σ_isos calculated in the default condition of DV-Xα method don't agree well to experimental ones. By optimizing AOs in a reasonable way, σ_isos were highly improved and agreed with experimental ones far better than results by Hartree-Fock (HF) method having conventional basis functions. The usefulness of MOs constructed with optimized numerical basis functions was clearly demonstrated.