We have studied sodium-ion conduction in complex hydrides NaAlH4 and Na3AlH6. The electrical conductivities of these complex hydrides were studied using ac impedance measurements at temperatures up to 363 K for NaAlH4 and 433 K for Na3AlH6. Nyquist plots obtained by the measurements indicated the sodium-ion conduction. Also, dc measurements showed that sodium-ion transference numbers of NaAlH4 and Na3AlH6 were almost unity. Na3AlH6 exhibited the sodium-ion conduction of 4.1 x 10(-4) S/cm at 433 K. This study will open up research on complex hydrides as solid-state sodium-ion conductors. 2012 American Institute of Physics. [doi:10.1063/1.3681362]