Cu ₂SnSe ₄compound, as a non-toxic inexpensive thermoelectric material, has low thermal conductivity and adjustable conductivity, which promises to have a high-efficiency thermoelectric application in a medium-temperature range. The Cu-doped bulk samples of Cu _{2+ x}SnSe ₄(0 ≤ x≤ 1) compounds are synthesized by a fast method, i.e. by combining high energy ball milling with spark plasma sintering. In this work, the thermoelectric properties of Cu-doped Cu ₂SnSe ₄compound are investigated. The experimental results reveal that the intrinsic vacancy at Cu/Sn site of Cu ₂SnSe ₄can be completely filled by Cu (i.e. x= 1 in Cu _{2+ x}SnSe ₄). The crystal structures of all Cu _{2+ x}SnSe ₄samples have the same space group F3 mas that of the undoped Cu ₂SnSe ₄. The electrical conductivity of Cu _{2+ x}SnSe ₄increases rapidly with the content of Cu doped at intrinsic vacancy increasing, concretely, it increases by two orders of magnitude and reaches a maximum value at x= 0.8. The increase in electrical conductivity results in the significant improvement in power factor. The observed results display that the increase in electrical conductivity is a nonlinear relationship with Cu-doping content in a range of 0 < x< 0.1, but is linearly related to the Cu-doping content in a range of 0.1 ≤ x≤ 0.8. Meanwhile, the carrier (hole) concentration is observed to reach a maximum value at x= 0.2 and then slightly decreases at x= 0.8. The rapid increase in electrical conductivity with Cu-doping content increasing may be attributed to the intensifying of Cu-Se bond network that plays a dominant role in controlling hole transport in Cu ₂SnSe ₄. The carrier mobility also increases with the Cu-doping content increasing in the range of 0 ≤ x≤ 0.8, which is in contrast to the common scenarios in thermoelectric materials that the carrier mobility decreases with the increase in the carrier concentration. Furthermore, the carrier transport mechanism of Cu _{2+ x}SnSe ₄sample is revealed to be able to be described by the small polaron hopping model, which means the strong coupling between electron and phonon. The analysis of thermal conductivities of the Cu _{2+ x}SnSe ₄samples reveals that the relationship between the electronic thermal conductivity and the electrical conductivity cannot be described by the classical Wiedemanmn-Franz law, which may be attributed to the formation of electron-phonon coupled small polaron. Therefore, the coupling between electron and phonon inside the Cu _{2+ x}SnSe ₄structure strongly influences the behaviors of carrier transmission and thermal conductivity.