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The effect of pressure on the low-temperature states of the Re₃Ge₇ is investigated by both electrical resistance and magnetization measurements. At ambient pressure, the temperature dependent resistance of Re₃Ge₇ behaves quasi-linearly from room temperature to above 60 K, then undergoes a two-step metal-to-insulator transitions (MIT) at temperatures T₁ and T₂ which may be related to a structural phase transition or occurrence of charge density wave (CDW) ordering. Upon applying pressure, a two-step (T₁, T₂) MITs split into 3 steps (T₁, T₂ and T₃) above 1 GPa, and all traces of MITs are fully suppressed at ~8 GPa. Subsequently, the SC shows a bulk nature at and above 12.2 GPa, where the SC T_c and H_c2 (onset) reach the maximum of T_c (onset) ~5.9 K and H_c2 (0 K) ~1.8 Tesla. Our results not only present the observation of SC under high pressure in Re₃Ge₇ but also provide a rich phase diagram associating the interplay between SC and different competing electronic states in the potentially topologically nontrivial system Re₃Ge₇.