In order to investigate the thermoelectric properties of $Zn_{k}$ $In_2$$O_{ 3＋k}$ homologous compounds, the samples of $Zn_{k}$ /$In_2$$O_{3＋k}$ / (k = integer between 1 and 9) were prepared by calcining the mixed powders of ZnO and $In_2$$O_3$fellowed by sintering at 1823 K for 2 hours in air, and their electrical conductivities and Seebeck coefficients were measured as a function of temperature in the range of 500 K to 1150 K. X-ray diffraction analysis of the sintered samples clarified that single-phase specimens were obtained for $Zn_{k} /$In_2$$O_{3＋k}$ with k = 3, 4, 5, 7, 8, 9. Electrical conductivity of the $Zn_{k}$ $In_2$$O_{3＋k}$ / decreased with increasing temperature, and decreased with increasing k for k $geq$ 3. The Seebeck coefficient was negative at all the temperatures for all compositions, confirming that $Zn_{k}$ $In_2$$O_{3＋k}$ / is an n-type semiconductor. Absolute values of the Seebeck coefficient increased linearly with increasing temperature and increased with increasing k for k $geq$ 3. The temperature dependence of the Seebeck coefficient indicated that Z $n_{k}$I $n_2$ $O_{3＋k}$ could be treated as an extrinsic degenerate semiconductor. Figure-of-merits of Z $n_{k}$I $n_2$ $O_{3＋k}$ were evaluated from the measured electrical conductivity and Seebeck coefficient, and the reported thermal conductivity. Z $n_{7}$ I $n_2$ $O_{10}$ has the largest figure-of-merit over all the temperatures, and its highest value was $1.5{ imes}$10$^{-4}$ $K^{-1}$ at 1145 K.5 K.