  We studied the electrical transport on $\beta$-Fe$_{4+\delta}$Se$_{5}$
single-crystal nanowires, exhibiting $\sqrt{5}\times\sqrt{5}$ Fe-vacancy order
and mixed valence of Fe. We observed a first-order metal-insulator transition
of the transition temperature at $\sim$28~K at zero magnetic field. The
dielectric relaxation reveals that the transition is related to an energy gap
expansion of $\sim$12~meV, involving the charge-orbital ordering. At nearly
28~K, colossal positive magnetoresistance emerges, resulting from the
magnetic-field dependent shift of the transition temperature. Through the
transition, the magnetotransport behavior transits from two-dimension-like to
one-dimension-like conduction. The transition temperature demonstrates
anisotropy with the $c$-axis as the preferred orientation in magnetic fields,
suggesting the spin-orbital coupling. Our findings demonstrate the novel
magnetoresistive transition intimating a topological transition in the
Fe-vacancy-ordered $\beta$-Fe$_{4+\delta}$Se$_{5}$ nanowires. The results
provide valuable information to better understand the orbital nature and the
emergence of superconductivity in FeSe-based materials.
