  We investigate the Einstein-Maxwell-scalar theory with a quasi-topological
term. Considering exponential couplings to Maxwell term, quasi-topological
term, and both terms, we obtain three sets of infinite scalarized charged black
holes by taking into account tachyonic instability of dyonic
Reissner-Nordstr\"{o}m black hole. Each set of infinite scalarized charged
black holes is classified by the number of $n=0,1,2,\cdots$, where $n=0$ is
called the fundamental black hole and $n=1,2,\cdots$ denote the $n$-excited
black holes. All $n=0$ black holes are stable against the radial perturbation,
while all $n=1,2$ black holes are unstable.
