La0.4Na0.6Fe2As2 single crystals have been grown out of an NaAs flux in an alumina crucible and characterized by measuring magnetic susceptibility, electrical resistivity, specific heat, as well as single-crystal x-ray and neutron diffraction. La0.4Na0.6Fe2As2 single crystals show a structural phase transition from a high-temperature tetragonal phase to a low-temperature orthorhombic phase at Ts=125 K. This structural transition is accompanied by an anomaly in the temperature dependence of electrical resistivity, anisotropic magnetic susceptibility, and specific heat. Concomitant with the structural phase transition, the Fe moments order along the a direction with an ordered moment of 0.7(1) μB at T=5 K. The low-temperature stripe antiferromagnetic structure is the same as that in other AFe2As2 (A = Ca, Sr, Ba) compounds. La0.5−xNa0.5+xFe2As2 provides a material platform for the study of iron-based superconductors where the electron-hole asymmetry could be studied by simply varying the La/Na ratio.