  A new theory of gravity called Eddington-inspired Born-Infeld (EiBI) gravity
was recently proposed by Ba\~{n}ados and Ferreira. This theory leads to some
exciting new features, such as free of cosmological singularities. In this
paper, we first obtain a charged EiBI black hole solution with a nonvanishing
cosmological constant when the electromagnetic field is included in. Then based
on it, we study the strong gravitational lensing by the asymptotic flat charged
EiBI black hole. The strong deflection limit coefficients and observables are
shown to closely depend on the additional coupling parameter $\kappa$ in the
EiBI gravity. It is found that, compared with the corresponding charged black
hole in general relativity, the positive coupling parameter $\kappa$ will
shrink the black hole horizon and photon sphere. Moreover, the coupling
parameter will decrease the angular position and relative magnitudes of the
relativistic images, while increase the angular separation, which may shine new
light on testing such gravity theory in near future by the astronomical
instruments.
