Nuclear magnetic shieldings were calculated with electron correlations through third order. The calculation was performed on the use of London’s gauge invariant atomic orbitals (GIAO) and the finite field many-body perturbation theory (FF-MBPT), in which the two kinds of perturbation fields, i.e., the external magnetic field and the field due to the nuclear magnetic moment, were introduced to get the perturbed one-electron states. The Hartree-Fock (HF) values and the second- and third-order Moller-Plesset (MP) correlation corrections of the nuclear magnetic shieldings were calculated in (i) four first-row hydrides HF, H2O, NH3, and CH4; and (ii) three linear molecules with a multiple bond N-2, CO, and HCN. The calculations showed that the post-HF correlations are important and much improve the calculated shielding values, and that the second-order corrections are positive, but the third-order ones are negative. Furthermore, the rovibrational corrections to the shielding constants in the HF molecule at 300 K Were estimated to be -9.9 ppm for F and -0.66 ppm for H.