The feasibility of realizing overscreened Kondo effect in ultra-cold Fermi gas of atoms with spin s ≥ 3 2 in the presence of a localized magnetic impurity atom is proved realistic. Specifying (as a mere example), to a system of ultra cold 22 Na Fermi gas and a trapped 197 Au impurity, the mechanism of exchange interaction between the Na and Au atoms is elucidated and the exchange constant is found to be positive (antiferromagnetic). The corresponding exchange Hamiltonian is derived, and the Kondo temperature is estimated at the order of 1 µK. Within a weak-coupling renormalization group scheme, it is shown that the coupling renormalizes to the non-Fermi liquid fixed point. An observable displaying multi-channel features even in the weak coupling regime is the impurity magnetization: For T ≫ TK it is negative, and then it increases to become positive with decreasing temperature.