  We have studied the electronic structure of $\beta$-Na$_{0.33}$V$_2$O$_5$,
which becomes a superconductor under pressure, by angle-resolved photoemission
spectroscopy. Clear band dispersions is observed only along the chain
direction, indicating the quasi-one-dimensional (1D) electronic structure. The
spectra of the V 3d band are dominated by a Gaussian-like broad feature at
$\sim$ 1 eV below the Fermi level ($E_F$) with negligible intensity at $E_F$,
which we attribute to strong electron-phonon coupling as in other 1D polaronic
metals. In the momentum space, the spectra show a maximum intensity at $k \sim
\pm \pi/4b$, where $b$ is the V-V distance along the b-axis, reflecting the
band filling of the chain and/or ladder.
