  Superconductivity frequently appears by doping compounds that show a
collective phase transition. So far, however, this has not been observed in
topological materials. Here we report the discovery of superconductivity
induced by Ga doping in orthorhombic Re$_{3}$Ge$_{7}$, which undergoes a
second-order metal-insulator-like transition at $\sim$58 K and is predicted to
have a nontrivial band topology. It is found that the substitution of Ga for Ge
leads to hole doping in Re$_{3}$Ge$_{7-x}$Ga$_{x}$. As a consequence, the phase
transition is gradually suppressed and disappears above $x$ = 0.2. At this $x$
value, superconductivity emerges and $T_{\rm c}$ exhibits a dome-like doping
dependence with a maximum value of 3.37 K at $x$ = 0.25. First-principles
calculations suggest that the phase transition in Re$_{3}$Ge$_{7}$ is
associated with an electronic instability driven by Fermi surface nesting and
the nontrival band topology is preserved after Ga doping. Our results indicate
that Ga-doped Re$_{3}$Ge$_{7}$ provides a rare opportunity to study the
interplay between superconductivity and competing electronic states in a
topologically nontrivial system.
