A Cu(I) complex with an asymmetric TTF derivative (CET-EDTTTF) is prepared from the slow-diffusion method using CET-EDTTTF and Cu(I)Br solutions and characterized by X-ray crystallography and EPR spectroscopy. Structural analysis shows Cu(I) ions are tetrahedrally coordinated to two bridging bromides, one terminal bromide, and one S atom from CET-EDTTTF. Detailed geometrical and EPR analysis identified that the dimmer molecule contains [Cu$_2Br_4]^{2-}$ anion between two [CET-EDTTTF]$^+$ radical cations. Single-crystal EPR investigation of the complex reveals that the ganisotropy is unusually big, compared to those of the previously reported TTF+ cation radicals, implying that there is significant contribution of the Cu d-orbital to the HOMO of the complex.