EuFe2As2 is a member of the ternary iron arsenide family. Similar to BaFe2As2 and SrFe2As2, EuFe2As2 exhibits a clear anomaly in resistivity near 200 K. It suggests that EuFe2As2 is another promising parent compound in which superconductivity may be realized by appropriate doping. Here we report the discovery of superconductivity in Eu0.7Na0.3Fe2As2 by partial substitution of the europium site with sodium. ThCr2Si2 tetragonal structure, as expected for EuFe2As2, is formed as the main phase for the composition Eu0.7Na0.3Fe2As2. Resistivity measurement reveals a transition temperature as high as 34.7 K in this compound, which is higher than the Tc of Eu0.5K0.5Fe2As2.