The quasirelativistic (QR) generalized unrestricted Hartree-Fock method for the magnetic shielding constant [R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys. 118, 1015 (2003); R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys.118, 1027 (2003)] has been extended to include the electron correlation effect in the level of the second-order Møller-Plesset perturbation theory (MP2). We have implemented the energy gradient and finite-perturbation methods to calculate the magnetic shielding constant at the QR MP2 level and applied to the magnetic shielding constants and the NMR chemical shifts of 125Te nucleus in various tellurium compounds. The calculated magnetic shielding constants and NMR chemical shifts well reproduced the experimental values. The relations of the chemical shifts with the natures of ligands, and the tellurium oxidation states were investigated. The chemical shifts in different valence states were explained by the paramagnetic shielding and spin-orbit terms. The tellurium 5p electrons are the dominant origin of the chemical shifts in the Te I and Te II compounds and the chemical shifts were explained by the p-hole mechanism. The tellurium d electrons also play an important role in the chemical shifts of the hypervalent compounds.