  The magnetic and magnetotransport properties of metallic 1$T$-VTe$_{2}$
single crystals were investigated at temperatures from 1.3 to 300 K and in
magnetic fields up to 35 T. Upon applying a high magnetic field, it is found
that the electrical resistivity displays a crossover from the logarithmic
divergence of the single-impurity Kondo effect to the Fermi liquid behavior at
low temperatures. The Brillouin scale of the negative magnetoresistivity above
the Kondo temperature $T_{\rm{K}}$ = 12 K indicates that the Kondo features
originate from intercalated V ions, with $S$ = 1/2. Both magnetic
susceptibility and Hall effect show an anomaly around $T_{\rm{K}}$. By using
the modified Hamann expression we successfully describe the
temperature-dependent resistivity under various magnetic fields, which shows
the characteristic peak below $T_{\rm{K}}$ due to the splitting of the Kondo
resonance.
