  We analyze the stability of scalarized charged black holes in the
Einstein-Maxwell-Scalar (EMS) theory with quadratic coupling. These black holes
are labelled 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.
We show that the $n=0$ black hole is stable against full perturbations, whereas
the $n=1,2$ excited black holes are unstable against the $s(l=0)$-mode scalar
perturbation. This is consistent with the EMS theory with exponential coupling,
but it contrasts to the $n=0$ scalarized black hole in the
Einstein-Gauss-Bonnet-Scalar theory with quadratic coupling. This implies that
the endpoint of unstable Reissner-Nordstr\"{o}m black holes with $\alpha>8.019$
is the $n=0$ black hole with the same $q$. Furthermore, we study the scalarized
charged black holes in the EMS theory with scalar mass $m^2_\phi=\alpha/\beta$.
