In a recent study, we showed by solid-state NMR that LiVPO4F, which is a promising material as positive electrode for Li-ion batteries, often exhibits some defects that may affect its electrochemical behavior. In this paper, we use DFT calculations based on the projector augmented-wave (PAW) method in order to model possible defects in this (paramagnetic) material and to compute the Fermi contact shifts expected for Li nuclei located in their proximity. The advantage of the PAW approach versus FP-LAPW we have been previously using is that it allows considering large supercells suitable to model a diluted defect. In the first part of this paper, we aim to validate the Fermi contact shifts calculation using the PAW approach within the VASP code. Then we apply this strategy for modeling possible defects in LiVPO4F. By analogy with the already existing homeotypic LiVOPO4 phase, we first replace one fluoride ion, along the VO2F4 chains, by an oxygen one and consider, in a second step, an association with a lithium vacancy. As a result, the agreement between the calculated NMR spectra and the experimental one is satisfying. In both cases, the local electronic structure and the spin transfer mechanisms from V3+ or V4+ ions to the Li nuclei are analyzed.