  A combined study of transport, thermodynamic, neutron diffraction, nuclear
magnetic resonance measurements and first principles calculation were performed
for $\beta$-V$_2$PO$_5$ single crystal. It was shown to be a semiconductor with
a band gap of 0.48 eV, undergoing a charge ordering (unusual V$^{2+}$ and
V$^{3+}$) phase transition accompanied by a tetragonal to monoclinic structural
distortion at 610 K and a paramagnetic to ferrimagnetic phase transition at 128
K with a propagation vector of $\textbf{k} = 0$. The easy axis is in the
monoclinic $ac$ plane pointing 47(9)$^\circ$ away from the monoclinic $a$ axis.
This collinear ferrimagnetic structure and anisotropic isothermal magnetization
measurements suggest weak magnetic anisotropy in this compound. The first
principles calculations indicate that the intra-chain interactions in the
face-sharing VO$_6$ chains dominate the magnetic hamiltonian and identify the
$\Gamma_5^+$ normal mode of the lattice vibration to be responsible for the
charge ordering and thus the structural phase transition.
