  The Eddington-inspired Born-Infeld (EiBI) gravity is a modification of the
theory of general relativity inspired by the nonlinear Born-Infeld
electrodynamics. The theory is described by a series of higher curvature terms
added to the Einstein-Hilbert action with the parameter $\kappa$. The EiBI
gravity has several interesting exact neutral and charged black hole solutions.
We study the problem of overcharging extremal black hole solutions of EiBI
gravity using a charged test particle to create naked singularity. We show that
unlike general relativity, the overcharging could be possible for a charged
extremal black hole in EiBI gravity as long as the matter sector is described
by usual Maxwell's electrodynamics. Once the matter sector is also modified in
accordance to the Born-Infeld prescription with the parameter $b$, the
overcharging is not possible as long as the parameters obey the condition $4
\kappa b^2 \leq 1$.
