Rotation of hyperfine fields at the V site in the multiband metal K2V8O6

51V nuclear magnetic resonance measurements are conducted on a single crystal of the mixed valence compound K2V8016 with 1.25 3d electrons per one V site. We determine the 51V Knight shift tensor, 51K, in the metallic state. 51K has the small anisotropy despite the conduction electrons in the anisotropic 3d orbitals. The principal axis of 51K rotates continuously on cooling temperature in the metallic state without breaking the lattice symmetry, I4/m. Taking into account the isotropic spin susceptibility, the thermal variation is attributed to a change in the hyperfine field tensor reflecting the 3d orbital shape.