We report on the implementation of an algorithm for the calculation of the NMR shielding tensor. Our scheme is based on the Hartree-Fock method and the zeroth-order regular approximation (ZORA) Hamiltonian with spin-orbital coupling included. Gauge-including atomic orbitals (GIAOs) are employed to ensure the origin invariance of the results. Unlike the previous implementation by Fukui and Baba [J. Chem. Phys. 2002, 117, 7836], our computational scheme makes use of Slater-type orbitals. We have employed this method in B3LYP calculations of the C-13, Pt-195, and Os-187 NMR chemical shifts in 5d metal carbonyls, Pt(H) square-planar complexes, and osmium phosphines, respectively. The calculated NMR chemical shifts are compared to the results obtained with the BP86 and BLYP functionals, as well as the Hartree-Fock method. Comparisons are also given to experimental values. For the Pt-195 chemical shifts, we have found a small improvement with respect to experiment for the B3LYP results. over the BP86 and BLYP values. For the other systems, use of the B3LYP method does not improve the agreement with experiment compared to results' from pure functionals such as BP86 and BLYP.