Searching　for　high-performance　thermoelectric　(TE)　materials　in　the　paradigm　of　narrow-bandgap　semiconductors　is　hampered　by　a　bottleneck.　Here　we　report　on　the　discovery　of　metallic　compounds,　TiFexCu2x-1Sb　and　TiFe1.33Sb,　showing　the　thermopower　exceeding　many　TE　semiconductors　and　the　dimensionless　figure　of　merits　zTs　comparable　with　the　state-of-the-art　TE　materials.　A　quasi-linear　temperature　(T)　dependent　electrical　resistivity　in　2-700　K　and　the　logarithmic　T-dependent　electronic　specific　heat　at　low　temperature　coexist　with　the　high　thermopower,　highlighting　the　strong　intercoupling　of　the　non-Fermi-liquid　(NFL)　quantum　critical　behavior　of　electrons　with　TE　transports.　Electronic　structure　analysis　reveals　a　competition　between　the　antiferromagnetic　(AFM)　ordering　and　Kondo-like　spin　compensation　as　well　as　a　parallel　two-channel　Kondo　effect.　The　T-dependent　magnetic　susceptibility　agrees　with　the　quantum　critical　scenario　of　strong　local　correlation.　Our　work　demonstrates　the　correlation　among　high　TE　performance,　NFL　quantum　criticality,　and　magnetic　fluctuation,　which　opens　up　directions　for　future　research.