The thermopower of a Luttinger liquid with a potential barrier is calculated. The long-range nature of the electron-electron interaction is taken into account. It is shown that an increase of the interaction range qualitatively changes the temperature dependence of the thermopower. At low temperatures, the Seebeck coefficient of the Luttinger liquid is significantly less than the corresponding coefficient of a one-dimensional Fermi gas. With increasing temperature, the thermopower increases rapidly and may exceed that of the Fermi gas. The results obtained are in qualitative agreement with experimental data for quasi-one-dimensional 5-nm-thick InSb wires.