An ab initio zeroth-order regular approximation (ZORA) theory for relativistic calculation of the nuclear magnetic shielding tensors is presented at the Hartree-Fock level. The nuclear magnetic shieldings tensors of hydrogen halides, HX (X=F, Cl, Br, and I), are calculated, and the results are compared to experimental values and other calculated results obtained using the Douglas-Kroll-Hess (DKH) transformation, the four-component random phase approximation (RPA), and the Dirac-Fock (DF) approaches. It is shown that the ZORA method underestimates the relativistic effects on the magnetic shieldings as compared to the four-component RPA results. However, as to the proton chemical shifts, the ZORA results are closer to the experimental proton shifts than those of the DKH and 4-RPA approaches.