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Single crystals of intermetallic Re₃Ge_7-xGa_x have been grown and characterized by measuring magnetization, electrical resistivity, thermoelectric power, and specific heat. For Re₃Ge₇, a phase transition at T_s = 58.5 K is indicated by a kink in magnetic susceptibility and is confirmed by a λ-like anomaly in specific heat. The temperature dependence of the electrical resistivity follows a typical metallic behavior above T_s and sharply increases below T_s, showing a metal-to-insulator-like transition. By substitution Ga for Ge-site, Re₃Ge_7-xGa_x, superconductivity emerges upon suppressing the phase transition. In the superconducting state for x ~ 0.4, the peak effect has been investigated by critical current (J_c) measurements in applied magnetic fields (H). The transition from a weakly pinned region to a strongly pinned region is mapped out in the H-J_c phase diagram.