We demonstrate thermoelectric transport properties of Zintl arsenide EuCuAs. The crystal structure of EuCuAs (hexagonal P63/mmc space group) consists of a covalently-bonded honeycomb-type [CuAs] network sandwiched by Eu2+ ions. Undoped EuCuAs exhibit the thermoelectric power factor of 1.2 and 0.4 mW/mK2 at 673 K along directions perpendicular and parallel to the uniaxial hot-pressing direction, respectively. Despite the relatively high power factor, dimensionless figure of merit is limited to 0.1 at 673 K due to the high lattice thermal conductivity, >2.0 W/mK. In addition to relatively high power factor, first-principles calculations predicted that, owing to a peculiar shape of the Fermi surface, heavy hole doped EuCuAs with hole concentration of >1.5 x 10^21 cm^-3 will exhibit the axis-dependent conduction polarity, which enables us to construct the transverse thermoelectric devices. We investigated the synthesis and thermoelectric transport properties of Eu1-xNaxCuAs using sodium (Na) as a hole dopant, resulting in a hole concentration of 1.0 x 10^21 cm^-3. The absolute value of the Seebeck coefficient decreased by Na-doping, as predicted by first-principles calculations, but no conduction polarity switching was observed. This may have resulted from insufficient hole concentration and/or preferred orientation of the samples.