  In this paper, we consider the tachyonic instability of Kerr-Newman (KN)
black holes in the Einstein-Maxwell-scalar (EMS) theory with nonminimal
negative scalar coupling to Maxwell term, and then obtain a bound
$(\frac{a}{r_+}\geq0.4142)$ for spin parameter $a$ of KN black hole in the
limit of coupling constant $\alpha\rightarrow-\infty$ by using analytical
method. In addition, we perform a $(2+1)$-dimensional time evolution of
linearized scalar field perturbation on the KN black hole background by
implementing the hyperboloidal foliation method numerically in the EMS theory.
It recovers the \textit{spontaneous scalarization} phenomenon for KN black hole
in some certain regions of the parameter spaces. We further plot corresponding
threshold curves $\alpha(a)$ which describe a boundary between bald KN black
holes and scalarized spinning black holes in the EMS theory.
