We present the first density functional theory based calculations of NMR shielding parameters for a transition metal nucleus using periodic boundary conditions. These calculations employ the gauge-including projected augmented-wave pseudopotential approach. The quality of this method is discussed by comparing experimental and calculated chemical shift tensor eigenvalues for the quadrupolar 51V nucleus in the diamagnetic solid-state compound AlVO4. Furthermore, the combination of shielding tensor with fast and accurate projector augmented-wave electric field gradient tensor calculations allows us to determine the relative orientation of these two tensors.