  We report the electrochemical performance of nanostructures of
Na$_{0.66}$V$_4$O$_{10}$ as cathode material for rechargeable batteries. The
Rietveld refinement of room temperature x-ray diffraction pattern shows the
monoclinic phase with C2/m space group. The cyclic voltammetry curves of
prepared half-cells exhibit redox peaks at ~3.1 and 2.6~V, which are due to
two-phase transition reaction between V$^{5+/4+}$ and can be assigned to the
single step deintercalation/intercalation of Na-ion. We observe a good cycling
stability with specific discharge capacity (measured vs. Na$^+$/Na) between 80
($\pm$2) and 30 ($\pm$2) mAh g$^{-1}$ at a current density 3 and 50~mA
g$^{-1}$, respectively. The electrochemical performance of
Na$_{0.66}$V$_4$O$_{10}$ electrode was also tested with Li anode, which showed
higher capacity, but decay faster than Na. Using density functional theory, we
calculate the Na vacancy formation energies; 3.37~eV in the bulk of the
material and 2.52~eV on the (100) surface, which underlines the importance of
nanostructures.
