Abstract: High-pressure-induced superconducting transition and structural phase transition have been observed in the higher-order topological insulator α-Bi₄Br₄. By means of <italic>in situ</italic> high-pressure Raman spectroscopy and anisotropic high-pressure electrical transport measurements, we systematically investigated the lattice dynamics and electrical transport evolution of this system. High-pressure Raman spectroscopy reveals that α-Bi₄Br₄ undergoes a structural phase transition from monoclinic <italic>C</italic>2/<italic>m</italic> to triclinic <italic>P</italic>-<italic>1</italic> in the pressure range of approximately 5.4-7.6 GPa. Electrical transport measurements along different crystallographic axes show that the superconducting zero-resistance state is established at 2.7 GPa along the quasi-one-dimensional chain direction (<italic>b</italic>-axis), while along the interchain direction (<italic>a</italic>-axis) it requires 3.4 GPa, exhibiting weak anisotropy; the superconducting transition temperature <italic>T</italic>_calong both directions is about 6 K.As the pressure is further increased to 8.1 GPa, a two-step superconducting transition emerges along the <italic>b</italic>-axis, signalling the appearance of a second superconducting phase (SC-II) with <italic>T</italic>_c≈ 8 K. Hall-effect measurements indicate that in the pressure range of 5.3-6.7 GPa, the dominant charge carriers change from electrons to holes, which is closely related to the Fermi-surface reconstruction driven by the structural phase transition. Combining all the above results, α-Bi₄Br₄ may host a coexistence of the SC-I superconducting phase and topological hinge states in the pressure range of approximately 2.7-5.4 GPa.The results deepen the understanding of the evolution of α-Bi₄Br₄ under high pressure and provide meaningful references for further exploration of topological superconducting states in this system.