Previous research on the ternary Ti-Fe-Sb system has revealed that stoichiometric TiFeSb cannot exist as a stable compound, whereas a single-phase TiFe_1.33Sb alloy with the half-Heusler-like structure has been synthesized by adding excessive Fe. In this work, we report that TiFeSb can also be stabilized by filling additional Cu to the vacant 4d site of the half-Heusler lattice. Our experiments indicate that the TiFeCu_xSb (x = 0–0.25) samples exhibit a p-type conduction with extremely high carrier concentration ((0.5 –2.5) × 10²² cm⁻³)), while these samples attain very large Seebeck coefficients, over 100 μV/K in the whole measured temperature range for the samples with x = 0.15–0.25. In addition, a logarithmic divergence of the temperature-dependent specific heat capacity (C_P/T) is observed at low temperatures, implying the strange-metal behavior of TiFeCu_xSb samples. The partial filling of the vacant 4d site results in significantly reduced lattice thermal conductivity, leading to the low total thermal conductivity of 2.8 W·m⁻¹·K⁻¹ at 823 K for the TiFeCu_0.20Sb sample. Consequently, a dimensionless figure of merit zT of 0.54 at 923 K is realized for TiFeCu_0.20Sb, demonstrating that promising thermoelectric materials with intriguing physical properties can be discovered in the composition gap of half- and full-Heusler alloys.