Recently, hole-doped GeSe materials have been predicted to exhibit extraordinary thermoelectric performance owing largely to extremely low thermal conductivity. However, experimental research on the thermoelectric properties of GeSe has received less attention. Here, we have synthesized polycrystalline Na-doped GeSe compounds, characterized their crystal structure, and measured their thermoelectric properties. The Seebeck coefficient decreases with increasing Na content up to x = 0.01 due to an increase in the hole carrier concentration and remains roughly constant at higher concentrations of Na, consistent with the electrical resistivity variation. However, the electrical resistivity is large for all samples, leading to low power factors. Powder X-ray diffraction and scanning electron microscopy/energy-dispersive spectrometry results show the presence of a ternary impurity phase within the GeSe matrix for all doped samples, which suggests that the optimal carrier concentration cannot be reached by doping with Na. Nevertheless, the lattice thermal conductivity and carrier mobility of GeSe is similar to those of polycrystalline samples of the leading thermoelectric material SnSe, leading to quality factors of comparable magnitude. This implies that GeSe shows promise as a thermoelectric material if a more suitable dopant can be found.