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

Scalarized black holes in the Einstein-Maxwell-scalar theory with a quasi-topological term