  The electronic structure of the first reported heavy fermion compound without
f-electrons LiV_2O_4 was studied by an ab-initio calculation method. In the
result of the trigonal splitting and d-d Coulomb interaction one electron of
the $d^{1.5}$ configuration of V ion is localized and the rest partially fills
a relatively broad conduction band. The effective Anderson impurity model was
solved by Non-Crossing-Approximation method, leading to an estimation for the
single-site Kondo energy scale T_K. Then, we show how the so-called exhaustion
phenomenon of Nozi\`eres for the Kondo lattice leads to a remarkable decrease
of the heavy-fermion (or coherence) energy scale $T_{coh}\equiv {T_K}^2/D$ (D
is the typical bandwidth), comparable to the experimental result.
